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Popular >

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

Solution

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

Solution

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

Solution steps

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

Solve linear ODE:

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

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

Popular Examples

y^{''}+5y=3cos(2t)

y^{^{''}} + 5 y = 3 cos (2 t)

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

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

(d^2y)/(dx^2)-1/5 (dy)/(dx)+3/400 =0

\frac{d ^{2} y}{d x ^{2}} - \frac{1}{5} \frac{d y}{d x} + \frac{3}{400} = 0

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

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

y^{''}+18y^'+81y=x

y^{^{''}} + 18 y^{^{'}} + 81 y = x

Frequently Asked Questions (FAQ)

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