General solution Definition and 303 Threads

When I realize that I am going to have a singular matrix (after exhausting row swap options and maybe even some elimination steps) what about the matrix tells me whether or not I can have a general solution?

Homework Statement Find the general solution of: a) sin x = 1/\sqrt{2} b) cos x = 0.5 The Attempt at a Solution a) x = asin(1/\sqrt{2}) x = (π/4) + 2nπ b) x = acos(0.5) x = π/3 + 2nπ Basically, my strategy was to solve for the basic angle, and then add multiples of the...

I need to solve d/dx(e^(-(x^2))*(du/dx))=u+x*(du/dx) I get e^(-(x^2))*u''-2xe^(-(x^2))*u'=u+x*u' u''-2x*u'=e^(x^2)*u+xe^(x^2)*u' u''+(2x-xe^(x^2))*u'-e^(x^2)*u=0 but I have no idea how to approach the problem from here. Can somebody please help?

Homework Statement I want to find the general solution of these two equations, \ddot{y}=\omega\dot{z} \ddot{z}=\omega\left(\frac{\mathbf{E}}{\mathbf{B}} - \dot{y}\right) Homework Equations These two equations are the result of quantitatively solving to find the trajectory of a charged...

Homework Statement getting gen sol of xy3zx+x2z2zy=y3z solve cauchy problem x=y=t, z=1/t The Attempt at a Solution i got gen sol F(C1,C2)=0 as C1=x/z, C2=y4-x2z2 i inserted t for x and y and 1/t for z and ended up with C1-2=1/(C22) I'm unsure what to do from...

Homework Statement y'''-3y'+2y=0 initial conditions y(0)=0, y'(0)=1,y''(0)=1 Homework Equations Assume y=e^{rt} The Attempt at a Solution By the substitution I'm left with r^3-3r+2=0 which gives me the roots of -2 and 1. my question is a lot of times with this type...

Homework Statement Solve y''+4y'+5y=0 find solutions for y(0)=1 and y'(0)=0 Homework Equations Quadratic equation The Attempt at a Solution Hows this look ? assume solution is in the form of y=ce^{rx} substitute y=ce^{rx} into the equation...

Im having trouble with this question. can anyone explain please? Homework Statement y'' + 6y' + 9y = x*exp(-3x)3x Homework Equations Find the general solution.

Homework Statement y' = \frac{y+y^2}{x+x^2} Homework Equations separation of variables The Attempt at a Solution I start with y' = \frac{y+y^2}{x+x^2} which is \frac{dy}{dx} = \frac{y+y^2}{x+x^2} next step is dy = \frac{y+y^2}{x+x^2}dx than I divide both sides by...

Homework Statement (x^2)yy' = e^x Homework Equations general solution to the DE The Attempt at a Solution first i changed y' to dy/dx (x^2)y(dy/dx) = e^x then divided both members by x^2 and multiplied both members by dx ydy = (e^x)dx/(x^2) or ydy = (x^-2)(e^x)dx...

I have this question, but don't know how to even start. Suppose (M) is a linear system of 2 equations and 3 unknowns, where (2,-3,1) its solution. Suppose (O) is a matching homogeneous linear system, where (-1,1,1) and (1,0,1) its solutions. How can I find the general solution of (M)? I'm...

Homework Statement y''+4y'+4y= t+exp(-2t) find the general solution for the differential equation Homework Equations The Attempt at a Solution general solution is sum of complementary function and particular integral frist finding complementary function y''+4y'+4y=0...

Homework Statement Find a general solution for y''' - 6y'' + 9y' = 0 Homework Equations The Attempt at a Solution I know that the general solution for a homogeneous DEQ is Y(x) = c1y1(x) + c2y2(x) ... cnyn(x) however, I am not given y1, y2 , or y3 so I am to assume that the...

Homework Statement This is really a maths problem I'm having. I need to get the general solution for the infinite square well in the form: u = A cos(kx) + B sin(kx) I found the general solution to be: u = A exp(ikx) + B exp(-ikx) Using Euler's formula: exp(ikx) =...

y''' + y' = tan(t) 0<t<pi I got yh = c1 + c2cos(t) + c3sin(t) I'm trying to solve by Undetermined Coefficient method and Variation of Parameters method, but it didn't work

Homework Statement Find the general solution y'' + 4y' +4y = 5xe^(-2x) The Attempt at a Solution I got (5/2)x^3*e^(-2x) as a particular solution. But I checked online at wolfram alpha and it says the particular solution is (5/6)x^3*e^(-2x). Using method of undetermined coefficients.

Question: find the general solution of xX' = aX i know it's kinda simple ode.. but, i just don't know y i can't get the correct answer.. solution.. xX' = aX x dX/dx = aX d/dx X = aX/x X = ∫aX/x dx X = aX ln |x| + C the general solution is Ax^a problem : i can't get the...

Homework Statement "find the general solution of the equation: y'' + 3y' + 2y = 0 characteristic is: r^2 + 3r + 2 = 0 solve quadratic: (r+2)(r+1) r = -2 r= -1 therefore GS of equation is: y = c_1e^-2x + c_2e^-x thanks for any help Homework Equations The Attempt at a Solution

ok well I'm pretty much home and dry in this problem the aim of this problem is to get the general solution for the ode below.. 2u'' - xu' + u = 0 = g(x) i started to solve it by rearranging the equation.. 2u'' + u = xu' apply Fourier transform.. 2F(u'') + u^ = g^ (-2k^2)u^ + u^...

[b] Find the general solution of the following ODE: dx/dt = 3x^(2) cos t [b] Make x the subject of the solution. [b] Heres my solution, is this correct? dx/dt = 3x^(2) cos t dx/3x^(2) = cos t dt Integrating both sides gives: ln (3x^(2)) = sin t + C 3x^(2) =...

Find y(t) assuming that y(0) = 4000 Homework Equations This is what I know! v = 20√10 x ((1+Ae^(t/√10))÷(1-Ae^(t/√10))) and A = -1 when finding particular solution to satisfy initial condition v(0). Terminal velocity = 63.246 m.s^-2 The Attempt at a Solution...

[b]1. Using separation of variables show that: v' = (cd/M)(v^2) - g has a general solution of: v = 20SQRT10 x ((1+Ae^(t/SQRT10)/(1-Ae^(t/SQRT10)) Homework Equations The Attempt at a Solution Have attempted numerous times with little success help appreciated!

If we assume air resistance is negligible, the only force acting on a body is -Mg where g is the acceleration due to gravity ( negative because acting downwards). F = Ma becomes : -Mg = M y'' which implies y[B]''=-g Question asks find the general solution for y. Homework Equations...

Homework Statement does this ode have a general solution? \frac{d^2 x}{d t^2} + \frac{k}{L -x} = 0 Homework Equations The Attempt at a Solution

At+1=(At+r)/(At+r+1) A1=constant I know I can set At+1=At=A and solve for a special solution. What would be a general solution? I am not taking a course in Difference Equation, and this is not my homework but I encounter a similar question and I reduce it to this form. Thanks

Homework Statement Find if it is true that the general solution to : y'' - y' = 0, where y(x), can be written as : y(x) = c1 cosh(x) + c2 sinh(x), where c1 and c2 are real arbitrary constants. Homework Equations differential equation solving The Attempt at a Solution I just...

This should be very simple, but I can find a simple example that violates my general conclusion. I clearly must be doing something wrong with my integration by parts. Any suggestions would be great. Define a distribution such that the density; \eta(\vec{x})=\int d\vec{k} f(\vec{x},\vec{k})...

Homework Statement Find the general solution to the system: ax+ by= 1 cx+ dy= 2 Consider the case when ad- bc \neq 0 The attempt at a solution Like in my other post, I multiplied the first equation by "c" and the second equation by "a", and then I subtracted the two equations. I...

Homework Statement Find the general solution to the system: ax+ by= 0 cx+ dy= 0 Consider the case when ad- bc\neq 0 The attempt at a solution I multiplied the first equation by "c" and the second equation by "a", and then I subtracted the two equations. I got the following...

Whenever I am stuck I usually manage by sitting down and working on the problem and eventuall finding the solution, this one is bothering me too much and I don't have any class until friday so no hope of finding out before then unless I ask here. Q: Find a general solution to the diff.eq...

Homework Statement \frac{d^{2}y}{dt} +4\frac{dy}{dt}+20y=e^{-2t}(sin4t+cos4t) Homework Equations The Attempt at a Solution The solution to the homogeneous equation: \frac{d^{2}y}{dt} +4\frac{dy}{dt}+20y=0 is y= k1e^{-2t}cos4t +k2e^{-2t}sin4t Then I guessed ae^{-2+4i} as a...

Morning everyone, Studying for a test and having a problem on a practice question he gave us to study with. Here's the question along with the answer: Y' = AY + [e^t e^-t 0] with A = [-1 0 4 -0 -1 2 0 0 1] the...

Homework Statement (D^2 + 2D + 10)^2 * (D^2 - 2D -3)y = 0. Homework Equations D = d/dx The Attempt at a Solution Solving for the roots gives: -1 + 3i, -1 - 3i <== both of multiplicity 2 and 3, -1. So the general solution should be: y = Ae^(3x) + Be^(-x) +...

General solution of initial value problem --dont understand problem is asking me?? Homework Statement Find a value for y-sub-0 for which the solution of the initial value problem: y' - y = 1+ 3sin t y(0) - y-sub-0 remains finite as t approaches infinity. (i called it "y-sub-0" , just...

Homework Statement This was a quiz problem Give the value of n and C for which y=Cx^n is a solution of the equation xdy/dx - 6y = 0Homework Equations ans n= 6 C= 0 (some triangle symbol) an n .. ineligible mark The Attempt at a Solution n = 6 C = All real numbers my tutor explained it...

Hello, The general solution of a differential equation for y'+P(x)y=G(x) is y(x)=e^{-\int P(x)dx}[C+\int e^{\int P(x)dx}G(x)dx] for y'+xy=x y(x)=e^{-\int xdx}[C+\int e^{\int xdx}xdx] i have y=Ce^{-\frac{x^2}{2}}+1 By the other solution \frac{dy}{dx}+xy=x \rightarrow...

Hi, I came across the following differential equation: \sqrt{1+(y')^2}=\frac{d}{dx}\left(y\frac{y'}{\sqrt{1+(y')^2}}\right) I found possible solutions: y\left(x\right)=cosh(x+C_{1}). However, this is a second order ODE so there exist a more general solution, with 2 freedom degrees...

Hi, I am just looking for clarification whether or not I am doing these problems correctly, here's an example: Homework Statement Find the general solution to x'' -2x' + 5x = 0 Homework Equations Charasteristic polynomial. Quadratic equation. General solution form for complex...

Homework Statement Find the general solution of the system of differential equations x'=10x - 12y y'=25x - 30y (where primes indicate derivatives with respect to t) by using the initial conditions x(0)=A y(0)=B Homework Equations The Attempt at a Solution x''=10x' - 12y'...

Homework Statement x''+13y'-4x=6sint , y''-2x'-9y=0 The Attempt at a Solution I am not really sure how to solve this completely, but I have done this so far: (D^2-4)x + 13Dy - 6sint = 0 , (D^2-9)y - 2Dx = 0 then I hit a brick wall. Any help would be appreciated, thanks.

Homework Statement Verify that the given functions form a fundamental set of solutions of the differential equation on the indicated interval. Form the solution. 4y^{''} - 4y^{'} + y = 0 e^{x/2}, xe^{x/2} Homework Equations...

Homework Statement Given that \nabla2 1/r = -4\pi\delta3(r) show that the solution to the Poisson equation \nabla2\Phi = -(\rho(r)/\epsilon) can be written: \Phi(r) = (1/4\pi\epsilon) \int d3r' (\rho(r') / |r - r'|) Homework Equations The Attempt at a Solution I know...

Homework Statement 81x^{2}y'' + 27xy' + (9x^{\frac{2}{3}}+8)y = 0 Hint: y = x1/3u x1/3 = z 2. The attempt at a solution Change of variables gives: \frac{d^{2}y}{dx^{2}} = x^{\frac{1}{3}}\frac{d^{2}u}{dx^{2}}+\frac{2}{3}x^{-\frac{2}{3}}\frac{du}{dx} - \frac{2}{9}x^{-\frac{5}{3}}u...

Homework Statement Quote: " PDE: ∂u/∂x + ∂u/∂y = 0 The general solution is u(x,y) = f(x-y) where f is an arbitrary function. Alternatively, we can also say that the general solution is u(x,y) = g(y-x) where g is an arbitrary function. The two answers are equivalent since u(x,y) = g(y-x) =...

dr/d(theta) + r*sec(theta) = cos(theta) apparently the solution is (sec(theta) + tan(theta))*r = theta - cos(theta) + c but i have no idea how to get there. i am using a technique from the book, but it yeilds an answer with lots of e's and an integral i can't solve. this is my work...

Homework Statement Solve for x using general solution sin2x = 0.5 Homework Equations sin2x= 2sinxcosx The Attempt at a Solution arcsin0.5 = 2x 2x = 30 degrees + k360 x = 15 degrees + k180. Or 2x = (180-30) + k360 2x = 150 + k360 x = 75 + k180

Homework Statement Claim: For the partial differential equation ∂u/∂x + ∂u/∂y = 0, the general solution is u(x,y) = f(x-y) Homework Equations N/A The Attempt at a Solution I remember that the number of arbitrary constants in the general solution should be the same as the order of the...

Hello, this is the first time I post here, I'm really stumped and tried everything, even my TI-89 calculator won't give me something nice XD Homework Statement Find the general solution of dy/dt= 1/(ty+t+y+1) Homework Equations No relevant equations. The Attempt at a...

I was interrested in the general solutions to the wave equation depending on only one spatial coordinate. For one linear coordinate, the general solution is: a f(x-ct) + b g(x+ct) For one radial spherical coordinate, the general solution is: a f(r-ct)/r + b g(r+ct)/r I thought that...

Problem:y' + y(1/x) = 3 x^2 y^2 Solution:p(x)= 1/x q(x) = 3x^2 <--- These are countinuous functions on the interval (0,+inf) y^-2[y' + y(1/x) = 3 x^2 y^2] A => y'y^-2 + y^-1(1/x) = 3x^2 v = y^(-n+1) = y^-1 v' = -y^-2 y' Plugin to problem A v' + v/x = 3x^2 B p(x) = 1/x...