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Popular >

y^{''}+3y^'+2y=3e^{-4t},y(0)=1

Solution

y^{^{''}} + 3 y^{^{'}} + 2 y = 3 e^{- 4 t}, y (0) = 1

Solution

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

Solution steps

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

Solve linear ODE:

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

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

Popular Examples

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

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

y^{''}+8y^'+16=0,y(0)=1,y^'(0)=0

y^{^{''}} + 8 y^{^{'}} + 16 = 0, y (0) = 1, y^{^{'}} (0) = 0

y^{''}-2y^'=6x+6-2e^{4x}

y^{^{''}} - 2 y^{^{'}} = 6 x + 6 - 2 e^{4 x}

y^{''}-4y^'+4y=15sin(x)-35cos(x)

y^{^{''}} - 4 y^{^{'}} + 4 y = 15 sin (x) - 35 cos (x)

y^{''}+9y=cos(2t),y(pi/2)=-1,y(0)=1

y^{^{''}} + 9 y = cos (2 t), y (\frac{π}{2}) = - 1, y (0) = 1

Frequently Asked Questions (FAQ)

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