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Popular >

y^{''}+y^'=t

Solution

y^{^{''}} + y^{^{'}} = t

Solution

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

Solution steps

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

Solve linear ODE:

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

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

Graph

Popular Examples

y^{'''}+y^{''}-2y^'=2+e^x-e^{5x}

y^{^{'''}} + y^{^{''}} - 2 y^{^{'}} = 2 + e^{x} - e^{5 x}

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

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

(D^{2} - 3 D) y = - 18 x

y^{''}-7y^'+12y=e^{3x}+e^{4x}

y^{^{''}} - 7 y^{^{'}} + 12 y = e^{3 x} + e^{4 x}

y^{''}+9y=e^{-2t}

y^{^{''}} + 9 y = e^{- 2 t}

Frequently Asked Questions (FAQ)

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