Find the particular integral of the differential equation d2y/dx2 + 3dy/dx + 2y = e −2x...

Find the particular integral of the differential equation

d²y/dx² + 3dy/dx + 2y = e ^−2x (x + 1). show that the answer is yp(x) = −e ^−2x ( 1/2 x² + 2x + 2) ]

Expert Solution

PLEASE RATE IF THIS WAS HELPFUL FOR YOU.

Colby Messinger answered 2 years ago

Find the particular integral of the following differential equations.(Explain each step clearly) (a) d2y/dx2 + y...

Find the particular integral of the following differential equations.(Explain each step clearly) (a) d2y/dx2 + y = (x + 1) sin x. show that the answer is yp(x) = − 1/8 [ (2x2 + 4x − 1) cos x − (2x + 2) sin x ] (Hint:In this case, we substitute sin αx or cos αx with eiαx then use the shift operator. In the case of sin αx we extract the imaginary part.)

Solve this differential equation (4x - 2y)dx + (2x - 9y)dy = 0

Consider the differential equation 2y^2+10y+12 = t+e^t Find the complementary function and particular integral. Hence write...

Consider the differential equation 2y^2+10y+12 = t+e^t Find the complementary function and particular integral. Hence write down the full general solution

Find the general solution of the differential equation (x + 2y) (dx-dy) = dx + dy.

differential equation y'=dy/dx = -(3xey+2y)/ (x2ey+x). find the solution

Find a particular solution of y'' + 2y' + y = e-x [ ( 5 −2x...

Find a particular solution of y'' + 2y' + y = e-x [ ( 5 −2x )cos(x) − ( 3 + 3x )sin(x) ] yp( x ) = ? Please show your work step by step. Thank you!

Solve Homogeneous differential equation. Please show work (4x - 2y)dx + (2x - 9y)dy = 0

Consider the curve given by the equation y^2 - 2x^2y = 3 a) Find dy/dx. b)...

Consider the curve given by the equation y^2 - 2x^2y = 3 a) Find dy/dx. b) Write an equation for the line tangent to the curve at the point (1, -1). c) Find the coordinates of all points on the curve at which the line tangent to the curve at that point is horizontal. d) Evaluate d 2y /dx2 at the point (1, -1).

Solving the differential equation given using indeterminate coefficients. a) y''+y'-6y=2x b) y''+2y'=2x+5-e^-2x

Solve the following differential equation by the method of undetermined coefficients: y′′ −2y′ +y=(2x)e^x +e^x(sin2x)

Question