General solution Definition and 303 Threads

Ok I'm new to ODE's so yeh, just to double check here's what I've done: Question: Find the general solution to the following differential equation: Equation: y'(x) = sec2 (3x + 1) My answer: Don't I just integrate? So dy/dx = sec2 (3x + 1) then, y = sec2 (3x + 1) dx so y = (tan(3x+1))/3

Homework Statement Find a general solution of the differential equation. (x+y)y' = x-y Homework Equations v=x+y y=v-x y'=v'-1 The Attempt at a Solution So if I plug this back into the original equation; v(v'-1)= x-y How do I convert v=x+y into x-y so that I have only v's...

The equation is y'' + 4y' + 4y = (3 + x)e-x and initial conditions y(0) = 2, y'(0)=5so from the associated homogenous equation I think the fundamental set of solutions is {e^-2x, xe^-2x} and so yc would be Yc = c1e-2x + c2xe-2x but now I don't know how to get Yp, particular solution or what...

Homework Statement For the system of differential equations \frac{dx}{dt}=(-3x-y) \frac{dy}{dt}=(-2x-2y) (a) Find the general solution. (b) Find the solution if x(0)=1 and y(0)=2. Homework Equations The Attempt at a Solution I have absolutely no clue how to do this. I have never seen a...

Homework Statement I was asked to find the general solutions of the two following differential equations: Q1. y'''[x] + 2 y''[x] + 5 y'[x] = 0 Q2. y''[x] + 6 y'[x] + 9 y[x] = 0 Homework Equations See above. The Attempt at a Solution My answers to both problems were of...

Homework Statement y''+4y'+3y=\sinh x, \, y(0)=y'(0)=0 The attempt at a solution The auxiliary equation is: m^2+4m+3=0 m= -3 and -1 The complementary function is: y_c=Ae^{-3x}+Be^{-x} I need to find the particular integral next. But i don't know what is the standard inverse D operator result...

If you are asked to solve a differential equation (single order) that has no initial values, then you separate if possible, integrate and include the Constant of integration, leaving the response in terms of the dependent variable, right? So if you are given a single order differential...

Homework Statement Find the general solution to the differential equation: (d2y/dx2) - 2(dy/dx) + y = 0Homework Equations The Attempt at a Solution Is my solution correct? (dy/dx) - 2 + (y^2)/2 + C1 = 0 y - 2y + (y^3)/6 + C1 + C2 = 0 -y + (y^3)/6 + C1 + C2 = 0 y = (y^3)/6 + C1 + C2 Thank you

I’m reviewing differential equations after taking the course about 5-6 years ago and I have a couple of questions about the solutions of differential equations. 1) First why is the general form of the solution to linear homogenous differential equations, with non-equal and real roots to the...

Homework Statement Solve: Ut=kUxx U(x,0)=e^3x Homework Equations The Heat Equation: The Attempt at a Solution g(y) in the heat equation for this problem is e^3y. I'm having serious trouble solving this because my professor hasn't taught us the method, and it isn't in the...

Homework Statement Find the general solution of the differential equation y'=4t-ty^2 Homework Equations y'=4t-ty^2 The Attempt at a Solution I 'think' this question is pretty straight forward but I'm still not sure if I did it right or not. I have two question. One till the last step...

Homework Statement find the general solution using integrating factors. xy' - 2y = 3x Homework Equations The Attempt at a Solution x(dy/dx) = 3x + 2y x*dy = (3x + 2y)dx (-3x + 2y)dx + xdy = 0 My = -3x + 2 Nx = 1 Not Exact (hence the use of integrating factors) μ(x)(-3x + 2y)dx + μ(x)xdy =...

Homework Statement Find the general solution to the following differential equations y'1 = -12y1 + 13y2 +10y3 y'2 = 4y1 - 3y2 - 4y3 y'3 = -21y1 +21y2 +19y3 The Attempt at a Solution I'm a little unsure about what to do at the end, or what form to put it in. The eigenvalues are λ1 =...

Hi, I don't understand why the general solution of 2nd order homogeneous equation is linear? Why is c_1e^(xt)+c_2e^(xt) a linear differential equation? What am I missing here? Any help would be appreciated, I'm struggling a bit understanding the concepts of differential equations...

Problem Statement Find the general solution to ty'-4y=(t^6)*(e^t) Solution Attempt I added the 4y over and divided by t y'=[(t^6)(e^t)+4y] / t I am not sure where to go from here. I'm pretty sure that separation of variables won't work, because I don't think that I can separate the 4y...

I am trying to solve the following problem and am a bit lost so any advice would be welcomed. x'' = 2x' + x = 3cos2t + sin2t My understanding is that I need to find the general solution for the unforced equation and a particular solution of the above equation. When these are added together...

Homework Statement Find an implicit, general solution to: dy/dx = (6x - 4y) / (x - y) with x > 0. Homework Equations The Attempt at a Solution dy/dx = (6x - 4y) / (x - y) x(dv/dx) + v = (6 - 4v) / (1 - v) [(1-v) / (v-3)(v-2)] dv = dx / x \int dv/(v-2) - 2\int...

Bernoulli -- Find the general solution Homework Statement Find the general solution of: y'+xy=xy^3 Homework Equations Bernoulli's Equation The Attempt at a Solution y'+xy=xy^3 (y^-3)y'+x(y^-2)=x Let v=(y^-2), thus v'=((-2y^-3)y' Then, -v'/2+xv=x Multiply...

Homework Statement 1) Determine the general solution of the equation 2) Use implict differentiation to verify that your solution satisfies the given PDE Homework Equations u u_x-y u_y=y The Attempt at a Solution \frac{dx}{u}=\frac{dy}{-y}=\frac{du}{y} Take the second two...

Hello, I need help with solving the following simultaneous equation. I tried using matrix solution using Gaussian elimination but it became too difficult early on. Known constants are a,A,b, and B. Known variables are x and y. Unknown variables are m and n. (a\timesx)/(A - x) +...

Homework Statement Find the general solution for a nonhomogenous equation. y''+4y=3csc2tHomework Equations The Attempt at a Solution I simplified the equation to... y''+4y=(3)/(sin(2t)) Then I guessed... y=Asint+Bcost y'=Acost-Bsint y''=-Asint-BcostThen I got...

dy/dt + y = \infty \sumSin(nt)/n^2 n=1 Ok still a bit new with all these symbols and stuff but that is the basic jist of it. y(t) = yh(t) + yp(t) it what i thought about using to start off with, yh(t) = Acos2t + Bsin2t. Then subbing yp(t) into the differential equation. Not really...

dy/dt + y =\infty\sumn=1Sin(nt)/n^2

dy/dt + y = Sigma Sin(nt)/n^2

Homework Statement Find the general solution for the following systems of equations, a solution to the initial value problem and plot the phase portrait. --> this is in matrix formx' = 1 2 0 3 all multiplied by x. also, x(0) = 2 -1 Homework Equations Determinant, etc.The Attempt at...

Homework Statement Find the general solution to y''-2y'-24y=50e6x-14cos(x)-175sin(x) Homework Equations I can't figure out how to solve for B,C,D, and E. I'm wondering if I did something wrong. The Attempt at a Solution I'm attaching photos, since it'd take forever to type this...

Homework Statement Find the general solution to x3y'''-9x2y''+76xy'=0 Homework Equations I'm kind of confused on where to start. I'd suppose you'd throw in y=emx but I'm not positive since there are Xs in there. Once I know what to do with the x terms, I can just find all the roots and that'll...

Homework Statement Find the general solution of dX/dt = AX(t) with the initial condition X(0) = (a1,a2,a3), where A = [0 1 0, 0 0 1, -1 1 1]. (Here, a comma signifies the end of a row). Homework Equations The exponential of A is e^A = ∑A^k/k! from k = 0 to k = ∞. The solution of dX/dt...

i want to know the general solution of dy/dx - y = x + 2x^2 i don't know how to do it. looked at every book. i can only do it when seperating the variables but here we have "-y"

Homework Statement y'' + cy' + 6y = 0 (where c is a constant) I need to find y(t) which i believe is the equation for a general solution. Homework Equations It would be r^2 + cr + 6y = 0 then I need to find the roots and create the general solution. My problem is I don't know what...

Homework Statement i have to create a general formula for integral of (x^n * e^x) dx using whatever method i deem appropriate. (the only way i could think of is by parts) Homework Equations int(x^n * e^x)dx int(uv')dx=uv-int(vu')dx The Attempt at a Solution i used integration by...

Homework Statement The question is: Homework Equations I really don't know what to put here but my method is: -Find det(A-\lambdaI) -Find the roots of the determinant - which are the eigenvalues -Solve for (X -(\lambda)I) I am stuck at this part The Attempt at a Solution...

Homework Statement If b =\sigma^2 > 0 (which implies b is real), then the general solution is Ce^(i\sigmax) + De^(-i\sigmax) = Esin(\sigmax) + Fcos(\sigmax) = Gcos(\sigmax + H). Homework Equations N/A The Attempt at a Solution So I know how to get the first two forms of the...

Homework Statement Find the general solution of the differential equation: y'' + 4y' + 13y' = 169x + 81e^{e-2x} EDIT: Can't get latex to work.. so : http://mathbin.net/60293 The Attempt at a Solution 13Ax + 4A + 13B + 9Ce^{-2x} = 169x+81e^{-2x} http://mathbin.net/60294 Now i have no clue...

[b]1. Find the general solution to sin3x+sin2x=0 [b]2. I am not sure what to use. I think the sin2x=2sinxcosx but I am unsure where to go from there [b]3. sin3x+2sinxcosx=0 unsure

Show that the "plane wave" is a general solution to the electromagnetic wave eqatuion Homework Statement Show that the "plane wave" E=Eocos(k.r-\omegat) is a general solution of the electromagnetic wave equation. (you must derive this first)Homework Equations we were given Maxwell equations...

Homework Statement If \psi(x) = Ae-ikx then the general solution \psi(x) = Asin(kx) + Bsin(kx) May I know if this is ODE? or? sorry, I need a refresher on my calculus. Homework Equations The Attempt at a Solution Homework Statement Homework Equations The Attempt at a Solution

Homework Statement Find the general solution of the given differential equation. Give the largest interval over which the general solution is defined. Determine whether there are any transient terms in the general solution. Homework Equations x(dy/dx) + 2y = 3 The Attempt at a...

Homework Statement Find a general solution. Homework Equations 2x\frac{dy}{dx}+y^{3}e^{-2x}=2xy The Attempt at a Solution Looks like a Bernoulli equation to me, after some algebra: \frac{dy}{dx}+\frac{y^{3}}{2xe^{2x}}=y \frac{dy}{dx}+\frac{y}{2xe^{2x}}=y^{-1} so with...

Homework Statement Question: I'm confused about how to app Find the real-valued general solution of the differential equation y''+1y'+1y=0 where primes indicate differentiation with respect to x. (Use the parameters a, b, etc., for undetermined constants in your solution.) The...

I am trying to solve this partial differential equation \frac{\partial^2 \rho (x)}{\partial x^2} + (ax+b)\frac{\partial \rho (x)}{\partial x} + c \rho (x) = const a, b and c are constant value. Could someone give me a general solution of this king of ode? Thanks in advance.

Homework Statement Find the general solution of: dy/dx=lnx/(xy+xy^3) Homework Equations The Attempt at a Solution In order to find the general solution, i rerrange the equation to:(y+y^3)dy=(lnx/x)dx, then int(y+y^3)dy=int(lnx/x)dx, then i got 2(lnx)^2=2y^2+y^4. then i rerange y...

i am having trouble finding the general solution for the given homogeneous equation: x2yy' = (2y2 - x2) which i made into x2dy = (2y2 - x2) dx i turned it into the following: (2y2 - x2) dx - x2 dy = 0 then i used substitution of y = xv and got (2(xv)2 - x2 - x2v) dx - x3 dv = 0 then...

Compute the general solution of the differential equation? dy/dt+1/t y = t*exp(-2t) y is outside 1/t can't seem to get it

I have x(t) = C(sub1) sin(16t) + C(sub2) cos(16t) Given: initial position x(0) = 1/6 so: 1/6 = C(sub1) sin(0) + C(sub2) cos(0) 1/6 = C(sub2) but how do i find C(sub1)? I am not given initial velocity

Homework Statement I need to find the solution to x'' + cx' = f(t), for a general f. Homework Equations The Attempt at a Solution Obviously first I solve the homogeneous part to give me A + B*exp(-ct). I also know that the particular solution is written as (1/c)int((1-exp(c(s-t))f(s))ds...

yIII+yII-yI-y = 0 I used the characteristic equation and got: r3+r2-r = 0 r (r2+r-1) = 0 Which means that r = 0 is one root, And the other factors from the polynomial are (-1-Sqrt(5))/2 and (-1+Sqrt(5))/2 This means that the final answer would be: y = C1 Exp(0x) + C2 Exp((-1-Sqrt(5))/2) +...

Homework Statement Let |\psi\rangle and |\psi '\rangle be solutions to the same Schrodinger equation. Show than, that c|\psi\rangle+c'|\psi '\rangle is the solution, where c and c' are arbitrary complex coefficients, for which holds: |c|^2+|c'|^2=1 The Attempt at a Solution Now this follows...

hi (y')^2+y^2=-2 why this differential equation has no general solution ?

Homework Statement http://img811.imageshack.us/img811/1989/problem1.png Homework Equations All shown in the above link, AFAIK The Attempt at a Solution Not worried about part a. For part b, when they say "assume the string is initially at rest" I took that to mean...