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Popular >

y^{''}+y^'=4t

Solution

y^{^{''}} + y^{^{'}} = 4 t

Solution

y = c_{1} + c_{2} e^{- t} + 2 t^{2} - 4 t

Solution steps

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

Solve linear ODE:

y = c_{1} + c_{2} e^{- t} + 2 t^{2} - 4 t

y = c_{1} + c_{2} e^{- t} + 2 t^{2} - 4 t

Graph

Popular Examples

y^{^{''}} - y + t^{2} = 0

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

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

y^{''''}+2y^{''}+y=3x+4

y^{^{''''}} + 2 y^{^{''}} + y = 3 x + 4

y^{''}-18y^'+81y=480sin(x)-210cos(x)

y^{^{''}} - 18 y^{^{'}} + 81 y = 480 sin (x) - 210 cos (x)

y^{''}+9y=2,y^'(0)=5

y^{^{''}} + 9 y = 2, y^{^{'}} (0) = 5

Frequently Asked Questions (FAQ)

What is the solution for y^{''}+y^'=4t ?
The solution for y^{''}+y^'=4t is y=c_{1}+c_{2}e^{-t}+2t^2-4t