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Popular Calculus >

y^{''}+2y^'-3y=x^2sin(x)

Solution

y^{^{''}} + 2 y^{^{'}} - 3 y = x^{2} sin (x)

Solution

y = c_{1} e^{x} + c_{2} e^{- 3 x} - \frac{x ^{2} sin ( x )}{5} - \frac{x ^{2} cos ( x )}{10} + \frac{x sin ( x )}{25} - \frac{7 x cos ( x )}{25} + \frac{29}{250} sin (x) - \frac{14}{125} cos (x)

Solution steps

y^{''} (x) + 2 y^{'} (x) - 3 y = x^{2} sin (x)

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- 3 x} - \frac{x ^{2} sin ( x )}{5} - \frac{x ^{2} cos ( x )}{10} + \frac{x sin ( x )}{25} - \frac{7 x cos ( x )}{25} + \frac{29}{250} sin (x) - \frac{14}{125} cos (x)

y = c_{1} e^{x} + c_{2} e^{- 3 x} - \frac{x ^{2} sin ( x )}{5} - \frac{x ^{2} cos ( x )}{10} + \frac{x sin ( x )}{25} - \frac{7 x cos ( x )}{25} + \frac{29}{250} sin (x) - \frac{14}{125} cos (x)

Graph

Popular Examples

y^{''}+5y=-9.81

y^{''}+4y^'+4y=3e^{-3x}

(d^2y)/(dx^2)+5(dy)/(dx)+6y=xe^{3x}

y^{'''}-4y^{''}+4y^'=x^2-e^{2x}

y^{''}+2y^'+2y=e^{-t}

Frequently Asked Questions (FAQ)

What is the solution for y^{''}+2y^'-3y=x^2sin(x) ?
The solution for y^{''}+2y^'-3y=x^2sin(x) is