Differential Equation : Homogeneous Solution

y'' + p(x)y' + q(x)y = r(x) has three solutions sin x, cos x, and sin 2x. Find yh. (yh is the corresponding homogeneous solution)

Find the solution (y sub p) to the following differential equation.

y'' + 2y' - 3y = e^(-3x) + x^2 * e^x

Differential Equations : Method of Undetermined Coefficients

Decide whether the method of undertermined coefficients can be applied to find a particular solutions of the given equations. (Explain) a) y'' + 3y' - y = tan x b) y'' + xy' + y = sin x

Differential Equations : Method of Undetermined Coefficients

Use the method of undetermined coefficients to solve the following differential equation. y'' + 2y' - 3y = 9x - 10 sin x y(0)=0 y'(0)=4

Differential Equation : General Solution

Please see the attached file for the fully formatted problems. Find a general solution on (-pi/2,pi/2) to y''+y=tan x given that S sec x dx = ln|secx + tanx|

Differential Equations

Please see the attached file for the fully formatted problems. y(t) + S t-->0 (t-tau)y(tau) dtau = e^t

Inverse Laplace Transform

Please see the attached file for the fully formatted problems.

Determine the Laplace transform of the function.

please see attachment

Exponential Order

Show that a) e^(t^2) is not of exponential order, and b) e^(t^1/2) is of exponential order

Find Laplace Transform of sin(t)/t

Find Laplace Transform of sin(t)/t. See attached file for full problem description.