General solution Definition and 303 Threads

Homework Statement Find the general solution f = f(x,y) of class C2 to the partial differential equation \frac{\partial^2 f}{\partial x^2}+4\frac{\partial^2 f}{\partial x \partial y}+\frac{\partial f}{\partial x}=0 by introducing the new variables u = 4x - y, v = y. Homework Equations...

If we have a function such as, $$e=\sum_{n=0}^{\infty} f(k)$$ Where 'k' can be (almost) any real value we choose and the summation series (although unique for each value of 'k') will always be equal to 'e' exactly, what do we call this?

Hello, I am learning about the general solution to higher order linear non-homogeneous differential equations. I know that the general solution of such an equation is of the form ##y=y_h+y_p## where ##y_h## is the solution to the respective homogeneous equation and ##y_p## is a particular...

Find the general solution of The ff. D.E 1.$\displaystyle (2xy-y^2+y)dx+(3x^2-4xy+3x)dy=0$ 2. $\displaystyle (x^2+y^2+1)dx+x(x-2y)dy=0$ i tried both of them using $\displaystyle \frac{\dfrac{\partial M}{\partial y}-\dfrac{\partial N}{\partial x}}{N}$ and $\displaystyle...

Does anyone know if we currently have an infinite series summation general solution for the gamma function such as, $$\frac{1}{\Gamma(k)}=\sum_{n=0}^{\infty} f(n,k)$$ or, $${\Gamma(k)}=\sum_{n=0}^{\infty} f(n,k)$$?

Homework Statement Find the general solution x(t) to the following differential equation: dx/dt = 2t/5xHomework Equations dx/dt = 2t/5x The Attempt at a Solution My solution is: ∫5xdx = ∫2tdt (5/2)x^2 = t^2 + C x^2 = (2/5)(t^2 + C) x = +-√[(2/5)(t^2 + C)] However, when I put the problem in...

Homework Statement The equation: \frac{dx}{dt}=\frac{t^2+1}{x+2}. Where the initial value is: x(0) = -2. Homework Equations I believe you have to use the method of seperations of variables. The Attempt at a Solution So I multiplied both sides with x+2. Then I integrated...

Hellow everybody! A simple question: exist a general formulation, a solution general, for a PDE of order 2 like: ## au_{xx}(x,y)+2bu_{xy}(x,y)+cu_{yy}(x,y)+du_x(x,y)+eu_y(x,y)+fu(x,y)=g(x,y) ## ? The maple is able to calculate the solution, however, is a *monstrous* solution!

It seems odd to me that we have no general solution to quintic equations yet. Is it possible that it exist any general solutions to equations of the fifth degree (and higher) that just haven't been discovered yet? Or are we certain that it doesn't exist?

Homework Statement The problem is attached as TheProblemAndSolution.png, and everything is typewritten, so it should be easily legible (but you will likely need to zoom into read the text since the image's height is significantly larger than its width). Homework Equations Differential...

Problem statement Given sin theta (sqrt 3)/2 Determine the domain for the following solution https://www.physicsforums.com/attachments/655052) determine each general solution using the angle measure specified. Revelant equations Attempt at solution1What is the reasoning behind that? For...

Hello, Homework Statement find the general solution to cos3θ = sin2θ Homework Equations The Attempt at a Solution I know that sinθ = cos(π/2 - θ) but I am unsure of how to apply this when I have sin2θ. Do I say that sin2θ = cos2(π/2 - θ)? I think not because when I do...

y"+2y'+y=2e^-t I tried to find the solution for this nonhomogenous diff. Equation but i could not. First i took a function Y(t)=Ae^-t but i was getting 0=2e^-t. To get rid of that i took another y'+y=2e^-t and found the solution y=2te^-t + ce^-t. Noticed that first part of this finding is...

Homework Statement Find the general solution for the current I(z,t) associated with the voltage V(z,t).Do this by substituting [1] into [2] and [3], integrate with respect to time, and then take the derivative with respect to z. Homework Equations V(z,t)= f+(t-z/vp) + f-(t+z/vp) [1]...

Hello - I asked a similar question before, but it was not resolved for me, and the person who answered was rude, so I did not continue the conversation. I read this here: http://tutorial.math.lamar.edu/Classes/DE/SecondOrderConcepts.aspx "If y_1(t) and y_2(t)are two solutions to a...

Homework Statement Prove that F(k•r -ωt) is a solution of the Helmholtz equation, provided that ω/k = 1/(µε)1/2, where k = (kx, ky, kz) is the wave-vector and r is the position vector. In F(k•r -ωt), “k•r –ωt” is the argument and F is any vector function. Homework Equations Helmholtz...

Find the general solution of x'=(2, 3, -1, -2)x+(e^t, t). (this is 2x2 matrix, 2 and 3 on the left, -1 and -2 on the right. and e^t on top, t on bottom. I know that the answer for 2x2 matrix is c1*(1, 1)e^t+c2*(1, 3)e^-t but I don't know how to get the other part.)

Express the general solution of x'=(1, 2, 3, 0, 1, 2, 0, -2, 1)x in terms of real-valued functions. (this is 3x3 matrix, 1, 2, 3 on the left, 0, 1, 2 in the middle, 0, -2 and 1 on the right. I found that the roots are 1, 1+2i, 1-2i. And a=2, b=-3, c=2 for the first root. a=0, b=1, c=i for the...

Express the general solution of x'=(2, 9/5, -5/2, -1)x in terms of real-valued functions. (this is 2x2 matrix, 2 and 9/5 on the left, -5/2 and -1 on the right. The complex roots are (1/2)+(3/2)i and (1/2)-(3/2)i and a=1, b=(3/5)+(3/5)i for the first root. And a=1, b=(3/5)-(3/5)i for the...

Express the general solution of x'=(3, 4, -2, -1)x in terms of real-valued functions. This is 2x2 matrix, 3 and 4 on the left, -2 and -1 on the right. I know that the eigenvalues are 1+2i, 1-2i. And a=1, b=1+i for the first eigenvalue. a=1, b=1-i for the second eigenvalue. But how do I get...

Homework Statement Find the general solution of (x+1)2y"+3(x+1)y'+0.75y=0 that is valid in any interval not including the singular point. Homework Equations y=xr y'=rxr-1 y"=r(r-1)xr-2 (x+1)2(r(r-1)xr-2)+3(x+1)(rxr-1)+0.75xr=0 The Attempt at a Solution What to do next?

Find the general solution of y"'-y"-y'+y=2e-t+3. Here's the work: r3-r2-r+1=r2(r-1)-(r-1)=(r-1)(r2-1)=(r2-1)2(r+1) r=1, -1 y=c1et+c2tet+c3e-t The answer in the textbook is y=c1et+c2tet+c3e-t+(1/2)te-t+3 but I don't know how to get the last 2 terms. Help me...

Find the general solution for: $$\left(\left(x^2+y^2 \right)x-y \right)\,dx+\left(\left(x^2+y^2 \right)y+x \right)\,dy=0$$

Homework Statement \cos x-\sqrt{3}\sin x=\cos(3x) Homework Equations The Attempt at a Solution Dividing both the sides by two i.e \cos x \cos \frac{\pi}{3}-\sin x \sin \frac{\pi}{3}=\cos (3x)/2 LHS can be written as ##\cos(x+\pi/3)##. Substituting ##x+\pi/3=t \Rightarrow...

I need help finding a linear homogenous constant-coefficient differential equation with the given general solution. y(x)=C1e^x+(C2+C3x+C4x^2)e-x 2. I tried to come with differential equation but this is it I can 't seem how to begin

I have searched for a long time and i can't find a clear answer I want to find the general solution for x^2*y''-2y=0 using deslove and i typed it in as desolve(x^2*y''-2y=0,y) and it says too few arguments then i tried desolve(x^2*y''-2y=0,y,x) same thing, then i switched the y ans the...

Homework Statement Find the general solution of the given differential equation: y''+y'+4y=2sinht Homework Equations I believe sinht=(e^t-e^-t)/2 The Attempt at a Solution I tried to find the general equation if it were homogenous however I get the roots are r=[1+-...

If this were the reduced row echelon form of an augmented matrix, 1 2 0 1 1 0 3 0 0 1 2 1 0 1 0 0 0 0 0 1 2 0 0 0 0 0 0 0 What is the form of the following answer given, and how can I understand it? (x1; x2; x3; x4; x5; x6) = (3; 0; 1; 0; 0; 2)+ t(1; 0; 1; 0; 1; 0)+ s(1; 0; 2; 1; 0...

I've been trying to get out this question for a while now: ai) Show that (x,y,z) = (1,1,1) is a solution to the following system of equations: x + y + z = 3 2x + 2y + 2z = 6 3x + 3y +3z = 9 aii) Hence find the general solution of the system b) Express 2x^2 + 3/(x^2 + 1)^2 in partial...

[b]1. The motion of a forced harmonic oscillator is determined by d^2x/dt^2 + (w^2)x = 2cos t. Determine the general solution in the two cases w = 2 and w is not equal to 2. To be honest I've no idea where to start!

Homework Statement Use substitution/elimination to find the general solution. dx/dt = 3x-y+2t^2 dy/dt = 4x-2y-8t^2 Homework Equations I'm practically clueless on how to solve this problem using substitution/elimination, I'm pretty sure the way I'm doing it is completely wrong. If anyone...

Homework Statement Find the general solution to ##A(x)y''+A'(x)y'+\frac{y}{A(x)}=0## where A(x) is a known function and y(x) is the unknown one. Hint:Eliminate the term that contains the first derivative. Homework Equations Not sure. The Attempt at a Solution So I don't really...

I have a differential equation of the form and I want to solve it using calculus, as opposed to using a differential equation method. \frac{d^2v}{dt} = \alpha where v is a function of t i.e., v(t) and \alpha is some constant. How do I solve for v(t) if the time ranges from t_0 to t...

Homework Statement Find the general solution to d2y/dx2 +4y=cos(2x) Homework Equations The Attempt at a Solution I have woked out what I think is the Complementary function C1sin(2x)+C2cos(2x) the reason it is cos and sin is because the roots are 2i and therefore the exponential...

Homework Statement Hey, guys. I'm having trouble finding the general solution to a second order, homogeneous ODE. It is the first step to solving an eigenvalue problem and my professor is about as much help as a hole in the head. I've tried multiple "guesses" and have combed various...

Before trying to find out the general solution of a radical equation; I would first like to know if it can be found? For example I have a equation of the form \text{A1}+\text{A2} x + \text{A3}\sqrt{\text{B1}+\text{B2} x+\text{B3} x^{\frac{3}{2}}+\text{B4}\sqrt{x}+\text{B5} x^2}+...

Hey, I'm trying to solve the following pde, u(x,y) u_x + u_y =0 with u(x,0) = p(x) for some known p(x) where u_x defines the partial derivative of u(x,y) wrt x after finding the characteristic curves and the first integrals i get the general solution is F(x^2 - zy^2, z) = 0...

General Solution for (x^2)*y"+x*y'-y=1/(x+1) Where do I start?

Homework Statement Find the general solution to: yii +y=sec2(t) The Attempt at a Solution I found the particular solution, which is Yp=-sec(t)cos(t)+ln|sec(t)+tan(t)|sin(t) Is the general solution just y(t)=C1cos(t)+C2sin(t)+Yp? I just can't find an example of an inhomogeneous problem with...

Find the general solution to the differential equation y'+(12x^11)y=x^12 Use the variable I= the integral of e^(x^12)dx where it occurs in your answer. According to some people, it doesn't have an elementary solution, look at...

Hi, my equation is; \frac{\partial}{\partial t}U(x,y,t) = 2g \left( x \frac{\partial}{\partial y} - y \frac{\partial}{\partial x} \right) U(x,y,t) I want to find the general solution to this but I don't know how to find it? Any help would be great...thanks :D

Homework Statement y'' - 3y' + 2y = e2xcos x The Attempt at a Solution So this is a second order inhomogeneous equation. gives λ = {2,1} get yCF giving Ae2x + Bex so yP = e2x(Ccosx + Dsinx) Here is where is gets a bit fuzzy. Subbing this into the top equation gives me 2e2x((-2D-C)cosx +...

General solution to a 2nd order differential :( Homework Statement What is the general solution of ∂2f(x,t)/∂x∂t = xt ? Homework Equations The Attempt at a Solution I have no idea, I tried to follow an example out of the book but it was quite different to this question. Do...

Hello, I have three differential equations, for these I have found the eigenvalues and eigenvectors. After that I made a vector general solution for the system of equations. From this vector, how can I predict the long term behaviour of the system? -Thanks.

Hi, I have the following PDE-S\frac{\partial\vartheta}{\partial\tau}+\frac{1}{2}\sigma^2\frac{X^2}{S}\frac{\partial^2\vartheta}{\partial\xi^{2}} + [\frac{S}{T} + (r-D)X]\frac{\partial\vartheta}{\partial\xi}I am asked to seek a solution of the form \vartheta=\alpha_1(\tau)\xi + \alpha_0(\tau)...

Hi everyone, I am doing a sheet on Asian Options and The Black Scholes equation. I have the PDE, \frac{∂v}{∂τ}=\frac{1}{2}σ^{2}\frac{X^{2}}{S^{2}}\frac{∂^{2}v}{∂ε^{2}} + (\frac{1}{T} + (r-D)X)\frac{∂v}{∂ε} I have to seek a solultion of the form v=α_{1}(τ)ε + α_{0}(τ) and determine...

Hello, I have the PDE \frac{-∂v}{∂τ}+\frac{1}{2}σ^{2}ε^{2}\frac{∂^{2}v}{∂ε^{2}}+(\frac{1}{T}+(r-D)ε)\frac{∂v}{∂ε}=0 and firstly I need to seek a solution of the form v=α_{1}(τ)ε + α_{0}(τ) and then determine the general solution for α_{1}(τ) and α_{0}(τ). I am given that ε=\frac{I}{TS}...

Homework Statement For the following differential equation: 1) Provide the general solution 2) Discuss for which values of x the solution is defined. 3) Find the solution of the initial value problem y(0) = 3Homework Equations dy/dx = (y+3)(y-5)The Attempt at a Solution 1) so I separate...

find general solution for differential equation dy/dt=2ty+4e^(t^2) i got e^(t^2)(4t+k) is that right?

Homework Statement Find the general solution near x = 0 of y'' - xy' + 2y = 0 (using power series). Answer: y = a_0 * y_1(x) + a_1 * y_2(x) where y_1(x) = 1 - x^2 and y_2(x) = x - 1/6 * x^3 - 1/120 x^5 - 1/1680 * x^7 - ... Homework Equations Power series. Sigma notation for...