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Popular >

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

Solution

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

Solution

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

Solution steps

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

Solve linear ODE:

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

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

Graph

Popular Examples

(d^2y)/(dx^2)+4(dy)/(dx)+5y=e^xcos(2x)

\frac{d ^{2} y}{d x ^{2}} + 4 \frac{d y}{d x} + 5 y = e^{x} cos (2 x)

4y^{''}-4y^'+y=32e^{t/2}

4 y^{^{''}} - 4 y^{^{'}} + y = 32 e^{\frac{t}{2}}

y^{'''}+6y^{''}+9y^'=6x+2

y^{^{'''}} + 6 y^{^{''}} + 9 y^{^{'}} = 6 x + 2

y^{'''}-6y^{''}+12y^'-8y=t^3e^{2t}+1

y^{^{'''}} - 6 y^{^{''}} + 12 y^{^{'}} - 8 y = t^{3} e^{2 t} + 1

y^{''}+4y=e^{3x}+xsin(2x)

y^{^{''}} + 4 y = e^{3 x} + x sin (2 x)

Frequently Asked Questions (FAQ)

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