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Popular >

y^{''}+3y^'+2y=e^{-4t},y(0)=0,y^'(0)=0

Solution

y^{^{''}} + 3 y^{^{'}} + 2 y = e^{- 4 t}, y (0) = 0, y^{^{'}} (0) = 0

Solution

y = (\frac{1}{2} - \frac{1}{6}) e^{- t} - \frac{1}{2} e^{- 2 t} + \frac{1}{6} e^{- 4 t}

Solution steps

y^{''} (t) + 3 y^{'} (t) + 2 y = e^{- 4 t}

Solve linear ODE:

y = (\frac{1}{2} - \frac{1}{6}) e^{- t} - \frac{1}{2} e^{- 2 t} + \frac{1}{6} e^{- 4 t}

y = (\frac{1}{2} - \frac{1}{6}) e^{- t} - \frac{1}{2} e^{- 2 t} + \frac{1}{6} e^{- 4 t}

Graph

Popular Examples

y^{''}+4y^'+3y=6e^{-5t}

y^{^{''}} + 4 y^{^{'}} + 3 y = 6 e^{- 5 t}

y^{''}+4y^'+5y=sin(sqrt(5)t)

y^{^{''}} + 4 y^{^{'}} + 5 y = sin (5 t)

y^{''}+4y^'+5y=2x-e^{-4x}+sin(2x)

y^{^{''}} + 4 y^{^{'}} + 5 y = 2 x - e^{- 4 x} + sin (2 x)

y^{''}+25y=32sin(3x+2)

y^{^{''}} + 25 y = 32 sin (3 x + 2)

y^{'''}-15y^{''}+500y=e^{10x}

y^{^{'''}} - 15 y^{^{''}} + 500 y = e^{10 x}

Frequently Asked Questions (FAQ)

What is the solution for y^{''}+3y^'+2y=e^{-4t},y(0)=0,y^'(0)=0 ?
The solution for y^{''}+3y^'+2y=e^{-4t},y(0)=0,y^'(0)=0 is y=(1/2-1/6)e^{-t}-1/2 e^{-2t}+1/6 e^{-4t}