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Popular >

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

Solution

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

Solution

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

Solution steps

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

Solve linear ODE:

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

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

Popular Examples

y^{''}-4y^'=8e^{6x}(x-1)

y^{^{''}} - 4 y^{^{'}} = 8 e^{6 x} (x - 1)

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

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

y^{'''}-3y^{''}+3y^'-y=x-8e^x

y^{^{'''}} - 3 y^{^{''}} + 3 y^{^{'}} - y = x - 8 e^{x}

(d^2y)/(dt^2)=0.5t-y

\frac{d ^{2} y}{d t ^{2}} = 0.5 t - y

y^{''}-y=e^xcos(x)

y^{^{''}} - y = e^{x} cos (x)

Frequently Asked Questions (FAQ)

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