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Popular >

y^{''}+2y^'=-y

Solution

y^{^{''}} + 2 y^{^{'}} = - y

Solution

y = c_{1} e^{- t} + c_{2} t e^{- t}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{- t} + c_{2} t e^{- t}

y = c_{1} e^{- t} + c_{2} t e^{- t}

Popular Examples

y^{''}+y=0,y^'(0)=-5

y^{^{''}} + y = 0, y^{^{'}} (0) = - 5

y^{''}+y^'=0,y(pi/3)=0,y^'(pi/3)=2

y^{^{''}} + y^{^{'}} = 0, y (\frac{π}{3}) = 0, y^{^{'}} (\frac{π}{3}) = 2

y^{''}-4y^'+4y=0,y(0)=3

y^{^{''}} - 4 y^{^{'}} + 4 y = 0, y (0) = 3

y^{''}-4y^'+4y=0,y(0)=0

y^{^{''}} - 4 y^{^{'}} + 4 y = 0, y (0) = 0

y^{''}-4y^'+4y=0,y(0)=1

y^{^{''}} - 4 y^{^{'}} + 4 y = 0, y (0) = 1

Frequently Asked Questions (FAQ)

What is the solution for y^{''}+2y^'=-y ?
The solution for y^{''}+2y^'=-y is y=c_{1}e^{-t}+c_{2}te^{-t}