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) ]

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Colby Messinger answered 1 year 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).

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

1. Evaluate the integral: ∫((e^(2x)−e^(−5x))^2+ ln(e^(1/x))) dx 2. Using cylindrical shells, find the volume of the...

1. Evaluate the integral: ∫((e^(2x)−e^(−5x))^2+ ln(e^(1/x))) dx 2. Using cylindrical shells, find the volume of the solid obtained by taking the region between y=x and y=x^2 for 1≤x≤3 and rotating it about the the line x=−4. 3. Find the average value of the function f(x) = 1/√x on the interval [0,4]. Then find c in [0,4] such that f(c) =f ave. please help!

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