2) Obtain a solution for the following: a) xạy” – 4y = 0 b)xy” + y...
4. The general solution of the differential equation a = xy + 4y is y= (b) - c+ 3 In/xl 2 ln x+c 4 In x + c - () None of these
Find the eigenvalues and eigenfunctions for the following
boundary-value problem.
xạy"+xy'+2y = 0, y'le')=0, y(1) =0)
Answer true or false without referring back to the text. The general solution of xạy" + xy' + (x2 – 4)y = 0 is y = C122(x) + cz?-2(X). True False
Use the reduction of order method to solve the following problem given one of the solution y1. (a) (x^2 - 1)y'' -2xy' +2y = 0 ,y1=x (b) (2x+1)y''-4(x+1)y'+4y=0 ,y1=e^2x (c) (x^2-2x+2)y'' - x^2 y'+x^2 y =0, y1=x (d) Prove that if 1+p+q=0 than y=e^x is a solution of y''+p(x)y'+q(x)y=0, use this fact to solve (x-1)y'' - xy' +y =0
27. Consider the Euler equation xạy" + a xy' + By = 0. Find conditions on a and B so that: a. All solutions approach zero as x → 0. b. All solutions are bounded as x → 0. c. All solutions approach zero as x + 0 d. All solutions are bounded as x + 00. e. All solutions are bounded both as x = 0 and as x → 00.
9. Solve the IVP with Cauchy-Euler ODE: xy"txy+4y-0; y(1)-o, y )--3 = 0 , use Variat 0 10. Given that y = GXtar2 is a solution of the Cauchy-Euler ODE x, "+ 2xy-2 Parameters to find the general solution of the non-homogeneous ODE y+2xy-y homogeneoury"rQ&)e-ar)-
Obtain the general solution to the equation. (x2+4) dx + xy-3x=0 The general solution is y(x) = 3, ignoring lost solutions, if any.
Consider the IVP y" - 4y' + 4y = 0, y = -2, y'(0) = 1 a. Solve the IVP analytically b. Using step size 0.1, approximate y(0.5) using Euler's Method c. Find the error between the analytic solution and the approximate solution at each step
Solve the Bernoulli equation a) xy′−4y = x^2√y, b) y′ = y(y^3 cosx +tgx), Solve the exact equation a) 2xcos^2 ydx +(2y−x2sin2y)dy = 0, b) (x^3 −3xy^2 +2)dx−(3x^2y−y^2)dy = 0, PLEASEEE it would mean a world to me
Exercise 7.3.8. In the following equations classify the point x = 0 as ordinary, regular singular, or singular but not regular singular. a. 2²(1+x?)y" + xy = 0 b. x+y" + y' +y=0 C. ng” +cº+y= 0 d. xy" + xy' - e"y=0 e. a’y" + xạy' + xạy=0