Consider the homogeneous second order equation y′′+p(x)y′+q(x)y=0. Using the Wronskian, find functions p(x) and q(x) such...

Consider the homogeneous second order equation y′′+p(x)y′+q(x)y=0. Using the Wronskian, find functions p(x) and q(x) such that the differential equation has solutions sinx and 1+cosx. Finally, find a homogeneous third order differential equation with constant coefficients where sinx and 1+cosx are solutions.

Expert Solution

Colby Messinger answered 1 year ago

find the general solution to the second order linear non-homogeneous differential equation (y"/2)-y' +y = cos...

find the general solution to the second order linear non-homogeneous differential equation (y"/2)-y' +y = cos x

Find the first-order and second-order partial derivatives of the following functions: (x,y) =x2y3

Consider the following second-order ODE, y"+1/4y=0 with y(0) = 1 and y'(0)=0. Transform this unique equation...

Consider the following second-order ODE, y"+1/4y=0 with y(0) = 1 and y'(0)=0. Transform this unique equation into a system of two 1st-order ODEs. Solve the obtained system for t in [0,0.6] with h = 0.2 by MATLAB using Euler Method or Improved Euler Method.

Find the general solution of the following second order linear equation. y'' + y = tan(x)

Use method of Frobenius to find one solution of Bessel's equation of order p: x^2y^''+xy^'+(x^2-p^2)y=0

Explain why the general solution of the Nonhomogeneous Second Order Linear Equation (NHSLE) y''+ p(x)y' +...

Explain why the general solution of the Nonhomogeneous Second Order Linear Equation (NHSLE) y''+ p(x)y' + q(x)y = f(x) has the form y = y_h + y_p where y_p is a particular solution and y_h is a general solution

Consider the equation y''− (sin x)y = 0. Find the general solution as a power series...

Consider the equation y''− (sin x)y = 0. Find the general solution as a power series centered at x = 0. Write the first six nonzero terms of the solution. Write the two linearly independent solutions that form the general solution. Differential Equations

a) Find the value of the Wronskian of the functions f = x^7 and g = x^8...

a) Find the value of the Wronskian of the functions f = x^7 and g = x^8 at the piont x = 1. b) Let y be the solution of the equation y ″ − 5 y ′ + 6 y = 0 satisfying the conditions y ( 0 ) = 1 and y ′ ( 0 ) = 2. Find ln ⁡ ( y ( 1 ) ). c) Let y be the solution of the equation y ″ + 2 y ′...

Consider the equation: x2 y''-6y=0 A. Could you solve this ODE using Homogeneous Linear Equations with...

Consider the equation: x2 y''-6y=0 A. Could you solve this ODE using Homogeneous Linear Equations with Constant Coefficients? Explain. B. Note that y1=x3 is a solution of the ODE. Using reduction of order, find a solution y2 such that { y1, y2} is linearly independent. C. Prove that{y1, y2} is linearly independent. D.What is the general solution?

Consider the second-order boundary value problem y′′ +(2x^2 +3)y′ −y =6x, 0≤x ≤1, (4) y(0) =...

Consider the second-order boundary value problem y′′ +(2x^2 +3)y′ −y =6x, 0≤x ≤1, (4) y(0) = 1, y(1) = 0. (a) Rewrite the second-order equation (4) as a system of two first-order equations involving variables y and z. [2] (b) Suppose that yn and zn are approximations to y(xn) and z(xn), respectively, where xn = nh, n = 0,...,N and h = 1/N for some positive integer N. Find the iterative formula when using the modified Euler method to approximate...

Question