General solution Definition and 303 Threads

Homework Statement determine the general solution of the equation: 2sinx +cosecx -3 = 0 Homework Equations The Attempt at a Solution Dont know what to do need help please.

Homework Statement Given: sec\theta=\sqrt{10} where 0< \theta <90 and \sqrt{10}sin(A-\theta)=sinA-3cosA Determine the solution of 6cosA +3 = 2sinA for A \in [-180; 180], rounded off to one decimal digit. Homework Equations The Attempt at a Solution 3=2sinA -...

Homework Statement h(x)=cos(x+30) and g(x) = -2sinx Determine the general solution without the use of a calculator, if h(x)=g(x) Homework Equations trig identities, trig ratios, double angle formulae, reduction formulae. The Attempt at a Solution cos(x+30)=-2sinx...

Homework Statement Find the general solution to the differential equation in implicit form. http://www.texify.com/img/%5Clarge%5C%21%5Cfrac%7Bdy%7D%7Bdx%7D%3D%28cosx-sinx%29e%5E%7Bcosx%2Bsinx%2By%7D.gif Homework Equations...

Homework Statement The question asks me to find the general solution to (x^2-1)y' + 2y = (x+1)^2, and to determine the largest interval over which this general solution is defined. It's the latter which is tripping me up. Homework Equations I've already found the general solution as...

Homework Statement Find the general solution of the following ODE: x^{2}Y''(x) + xY'(x) - CY(x)=0 where C is a constant. Homework Equations The Attempt at a Solution First I want to do this in the case where C=0; this gives: x^{2}Y''(x) + xR'(x)=0 How do i solve this...

Homework Statement Find the general solution of the differential equation, y' + y = be^(-λx) where b is a real number and λ is a positive constant. Homework Equations y' + P(x)y = Q(x) Integrating factor: e^(∫P(x) dx) The Attempt at a Solution Let P(x) = 1, Q(x) =...

Homework Statement Find the general solution of the first-order differential equation, y' + 3y = 2xe^(-3x) Homework Equations y' + P(x)y = Q(x) Integrating factor = e^(∫P(x) dx) The Attempt at a Solution Since it's already in the form y' + P(x)y = Q(x), the integrating...

Homework Statement Find the general solution of the differential equation specified. \frac{dy}{dt} = ty. The Attempt at a Solution I already know the answer to be ke^{t^{2}/2}, but can't figure out how it got here. I'm rusty with my integrals and am just really starting diff eqs...

1. Homework Statement + relevant equations I have to solve http://home.vs.moe.edu.sg/linl/eqn1.gif sigma, pinfinity, rho, N are constants. To make things easier for us, we are allowed to treat T as a constant. 2. The attempt at a solution Treat T as constant...

Homework Statement Find the general solution of (D^4 - I)^2(D^2 - 4D + 13I)^2(y) = 0 2. The attempt at a solution My issue with this problem is that I have no clue as to what the I's mean. I have become familiar with D being used notationally with differential equations, but the...

1. The problem statement Given the general solution: y==(2*c*e^(2x)) / (1+c*e^(2x)) find the EDO. 2. The attempt at a solution Im tried isolate c*e^(2x), using implicit differentiation: y + y*c*e^(2x)==2*c*e^(2x) y'+y'*c*e^2x + 2*y*c*e^(2x)==2*2*c*e^(2x) y'==c*e^(2x) * (4-y'-2y)...

I was just wondering, if I had a matrix in reduced-row echelon form, say, 1 0 0 2 0 1 3 1 0 0 0 0 then I could write the general solution as a1= -2a4 , a2= -3a3-a4, with a3 and a4 defined in terms of these. (I obtained this solution by putting a1, a2, a3 and a4 under the first...

I have Abel equation of second type. I've found one particular solution for sure, maybe two. Is it possible to construct the general solution from those with integration or whatever? I know that is possible for Ricatti ODE and since Ricatti is particular case of Abel, I was wondering if...

Homework Statement Find the general solution to Laplace's equation in spherical coordinates, for the case where V depends on on r. Do the same for cylindrical coordinnates assuming V depends only on r. Homework Equations Laplace's Eq (spherical): 1/r^2 (d/dr)(r^2(dV/dr)) +...

Hi all. Can the general solution of a linear ordinary differential equation be expressed in terms of its initial conditions? It seems that I have seem this kind of representation. It makes "some sense" to me but I hope to know if there is some "proof" or explanation of why it can be? To be...

Homework Statement Hi all. I have the following equation containing the variables x and y, where A, c > 0 and B is a constant, which I am not told anything about: -c^2x^2+y^2+2By+A=0. I wish to find two solutions {x_1, y_1} and {x_2, y_2}, to this problem and they must be linearly...

starting with question of find the general sollution of the differential equation X2y'=y2+3xy+X2 would an acceptable answer be y=-x(ln|x|+c+1) i would show all my working but my camera isn't working so i'll save you must the trouble and just skip to a part that i know is correct where...

Homework Statement 2xy" + y' + xy =0 xo=0 find the indicial equation, recurrence relation and series solution. Homework Equations The Attempt at a Solution I've done most of the work but i don't know how to use a recurrence relation to obtain a y1 and y2 series solution...

y''+xy'+y=0 PS: Is there a way to prove that one has found the "most" general solution by only using a particular method (e.g., integrating factors), with the possiblity of obtaining a different general solution using a different method? For example, using integrating factor in the ODE...

Find the general solution of the ordinary differential equation. y'' - 7y'+ 6y = 2e^(3t) + te^(t) First i found GS(H) by lettings y = e^(cx) and got GS(H) = Ae^(6t) + Be^(t) i then found PS(IH) y'' - 7y'+ 6y = 2e^(3t) by letting y = ae^(3t) and got PS(IH) = -(1/3)e^(3t) Now my...

\sum^{\infty}_{r=0}\frac{Tb_r}{r+n+1} = {[\sum^{\infty}_{r=0}\frac{b_r}{r+1}]}^{n} T is a constant . latex needs to be improved deeply :)

Im looking for a general solution to the following equation but i can't seem to get an answer. 3xdy = (ln(y^{6}) - 6lnx)ydx I've got this far anyway.. \frac{3x}{y} dy = (ln(y^{6})-ln(x^{6})) dx \frac{dy}{dx} = \frac{y}{3x} . 6ln\frac{y}{x} \frac{dy}{dx} = \frac{y}{x} ...

What if I have the general solution and I want to find the differential equation where it came from? Say for example my general solution is y=sin(ax + b) with a and b constants. How could I find the differential equation?

Homework Statement Given the matrix A=[...], find the general solution of; A[x;y;z]=[0;0;0] Homework Equations The Attempt at a Solution This question has me lost. When I look at that it tells me x, y and z are all equal to 0. Is there something I'm missing, perhaps in the words...

im asked to find the general solution to the equation below and after find the implicit form I've done some work on it and just wanted to see if I am going in the right direction. the equation dy/dx = e^-3y cos x (1+sin x )^2 My attempt at a general solution 1/3 e^3 = (sin x...

Is there a general solution for gravity force in Alderson Disk system? Given: Alderson Disk system, disk inner radius R1, outer radius R2, thickness T, density Rho, star mass M (irrelevant due to superposition?). http://orbides.1gb.ru/orbf/ad1.jpg How to find amount and direction of...

[b]1. The question asks me to show that e^x is a solution of xy'' - (2x+1)y' + (x+1)y=0 and find the general solution. [b]2. I managed to simplify the equation to u''xe^(x) - u'e^(x) = 0 by letting y=ue^(x) and finding the differentials and substituting them in. I've then let z=u...

Hi, I'm having a bit of trouble with a problem here. The question is: Use the Method of undetermined coefficients to Find the general solution to th system: dx/dt = y + e^t dy/dt = -2x + 3y + 1 I've got the homogenous solution fine, however I'm having a bit of difficulty with the...

Homework Statement Find the general solution of the following differential equation: x.(dy/dx) = y + sqrt.[(x^2) - (y^2)] Homework Equations I'm working through my excerise book and have been able to get through quite a few differential equations with success, but this one really does...

Homework Statement Find the PDE for this general solution: U(x,y) = Phi(x+y) + Psi(x-2y) Homework Equations The Attempt at a Solution I let my xi = x+y and my eta = x-2y and found that both roots are {-1,1/2}. From that I multiplied: (dy/dx - root1)*(dy/dx - root2) to give me the...

Hello, I'm writing an application for a java class that solves the problem where you are given n jugs of arbitrary sizes and have to come up with the steps to reach a certain value. I have figured out(read: did research) how to do this in a different way than the original, but it requires...

I have a question that involves a system of equations that I can't figure out Give the general solution of the set of equations below: x'=2x y'=-x+3y z'=2x-4y+6z Hint: While you can use eigenvalues and eigenvectors for this one, there is an easier way to do it. That's where I'm...

First it asks a few questions about what if it were a classical particle approaching the barrier. Much of this I understand and am OK with. Then we start treating the particle as a quantum thing so its governed by the TI Schrodinger EQ. So, what it wants me to do which I am a bit unsure about...

Howdy, I have been asked to find the general solution of the following matrix (pic attached). The matrix does not have an inverse, so I am a bit confused guys. Cheers and thanks in advance!

Hi, can someone please help me with the following ODE? I need to find the general solution. y = xy' + \frac{1}{{y'}} Rearranging I get a quadratic in dy/dx. x\left( {\frac{{dy}}{{dx}}} \right)^2 - y\left( {\frac{{dy}}{{dx}}} \right) + 1 = 0 \frac{{dy}}{{dx}} = \frac{{y \pm...

assuming that the circuit will lead to infinite, but converging, and R1,R3,R5 are in increasing magnitude, R2 is constant, is there a general formula for this problem?

Here is my question Find the general solution to the differential equation y''-18y'+80y=0 Express the solution in terms of the variable t. Give the smaller root first. My problem is that I don't know what general solution mean? what does it mean? And where does the t come from?

1) I need to find the general solution, using the method of seperating the variables of the following diff Equ: dy/dx = (2xcos x)/y where y>0 Is the answer = 2(cos x + xsinx) 2) If y = 2 when x = 0, find y in terms of x Could someone help me on this one 3) Explain why your answer...

These are differential equations problems. They are now "redo's", so I have hints from the grader that I don't understand. First problem: (x^2 + 1)y'' + 6xy' + 4y = 0 After isolating C_n+2, I have this. (n+2)(n+1)C_n+2 * X^n = -n(n-1)C_n * X^n - 6nC_n * X^n + 4C_n C_n+2 = [-n(n-1)C_n - 6nC_n +...

hi all, how do you find the particular integral of \ddot{c} + \alpha c = \frac {\lambda L} {2lm} - g I can find the complementary function of the above. Not sure what to do from here tho.

I have a 2nd order homogenous P.D.E: (d^2)V/((dx)^2) + (d^2)V/((dy)^2) + 6(d^2)V/(dx dy) = 0 where all derivatives are partial derivatives. I need to transform this to form a*(d^2)f/(dX^2) + b*(d^2)f/(dY^2) = 0 where a, b are constants and the derivatives are again partial, and f(X,Y) =...

why does the general solution to the euler-cauchy equation only work for x>0?

For the general solution of sin x = 0, must you have a solution using 0, pi and 2pi (ie. pi + 2pi * k, 2pi + 2pi * k, ...) or does using pi suffice?

could some1 help me with the working of this question. it's for homework and i would help if i knew how to come to the answer in the back of the book. it says to find the general solution (y=...) given y'(x) = 2/(7-4y) ... how do u get to this: y = 7/4 +/- √(k-x) that is...

Hi can someone help me out with the following question? Q. The differential equation for unforced under-damped oscillatory motion can be written \mathop x\limits^{..} + 2p\mathop x\limits^. + \omega ^2 x = 0 where the constants p and omega satisfy 0 < p < \omega . Find the general...

I discovered the following general solution to primitive forms of y^2 + 2x^2 = a^2 a = 3 + 4n(n+1) y = 4n(n+1) - 1 x = 4n + 2 Moreover let P = {11, 17, 19, 41, 43 ...} = the set of prime divisors of numbers of the form 3+4n(n+1) without the 3, and let Q = { -1, 7, 17, 23 ...} = the set of...

Diff. Eq. Problem ---> y'' - 2y' - 3y = -3 t e^(-t) What is general solution? This is problem number 3 in section 3.6 in Boyce, DiPrima 8th Edition "Elementary Differential Equations and Boundry Value Problems" Find the general solution of the differential equation: y'' - 2y' - 3y = -3 t...

General solution for a trigonometry equation. I solved this equation with several method and I found two possible expressions for the answers. They should be exactly the same. Please help me check for them or combine them together to give the one which is more common. Thanks for any ideas...

I worked out this problem from Griffith's book. The problem is to find the general expression for \nabla(r^n). This is how I worked it out: If \vec r = \hat x x+\hat y y+\hat z z r is the separation vector whose magnitude is given by \sqrt{x^2+y^2+z^2} Hence r^n =...