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Popular >

y^{''}+2y^'-3y=5e^xsin(2x)

Solution

y^{^{''}} + 2 y^{^{'}} - 3 y = 5 e^{x} sin (2 x)

Solution

y = c_{1} e^{x} + c_{2} e^{- 3 x} - \frac{1}{4} e^{x} sin (2 x) - \frac{1}{2} e^{x} cos (2 x)

Solution steps

y^{''} (x) + 2 y^{'} (x) - 3 y = 5 e^{x} sin (2 x)

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- 3 x} - \frac{1}{4} e^{x} sin (2 x) - \frac{1}{2} e^{x} cos (2 x)

y = c_{1} e^{x} + c_{2} e^{- 3 x} - \frac{1}{4} e^{x} sin (2 x) - \frac{1}{2} e^{x} cos (2 x)

Popular Examples

y^{''}-4y^'+5y=e^2x,y(0)=1,y^'(0)=3

y^{^{''}} - 4 y^{^{'}} + 5 y = e^{2} x, y (0) = 1, y^{^{'}} (0) = 3

8y^{''}-y^'+y+x^2=0

8 y^{^{''}} - y^{^{'}} + y + x^{2} = 0

y^{'''}-9y^{''}+27y^'-27y=8e^{3x}

y^{^{'''}} - 9 y^{^{''}} + 27 y^{^{'}} - 27 y = 8 e^{3 x}

(d^2x)/(dt^2)+81x=8sin(9t)

\frac{d ^{2} x}{d t ^{2}} + 81 x = 8 sin (9 t)

(d^4y)/(dt^4)-y=3t+cos(t)

\frac{d ^{4} y}{d t ^{4}} - y = 3 t + cos (t)

Frequently Asked Questions (FAQ)

What is the solution for y^{''}+2y^'-3y=5e^xsin(2x) ?
The solution for y^{''}+2y^'-3y=5e^xsin(2x) is y=c_{1}e^x+c_{2}e^{-3x}-1/4 e^xsin(2x)-1/2 e^xcos(2x)