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Popular >

y^{''}-2y^'+y=(e^t)/(t^2+1)

Solution

y^{^{''}} - 2 y^{^{'}} + y = \frac{e ^{t}}{t ^{2} + 1}

Solution

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

Solution steps

y^{''} (t) - 2 y^{'} (t) + y = \frac{e ^{t}}{t ^{2} + 1}

Solve linear ODE:

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

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

Graph

Popular Examples

y^{'''}+y^{''}+y^'+y=e^{-t}+13t

y^{^{'''}} + y^{^{''}} + y^{^{'}} + y = e^{- t} + 13 t

y^{''}+y^'-6y=-3sin(x)+4e^{2x}

y^{^{''}} + y^{^{'}} - 6 y = - 3 sin (x) + 4 e^{2 x}

(d^2y)/(dt^2)+4(dy)/(dt)+4y=te^{2t}

\frac{d ^{2} y}{d t ^{2}} + 4 \frac{d y}{d t} + 4 y = t e^{2 t}

y^{''}-25y=sinh(5x)

y^{^{''}} - 25 y = sinh (5 x)

y^{''}+y^'-12y=e^x+e^{2x}-1

y^{^{''}} + y^{^{'}} - 12 y = e^{x} + e^{2 x} - 1

Frequently Asked Questions (FAQ)

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