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Popular >

y^{''}+y^'=e^x

Solution

y^{^{''}} + y^{^{'}} = e^{x}

Solution

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

Solution steps

y^{''} (x) + y^{'} (x) = e^{x}

Solve linear ODE:

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

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

Popular Examples

integral of 1/(x^{-1)}

\int \frac{1}{x ^{- 1}} d x

(dy)/(dt)=y(10-y)

\frac{d y}{d t} = y (10 - y)

(\partial)/(\partial x)(cos(θ))

\frac{\partial}{\partial x} (cos (θ))

area y=-x-1,x=-1,x=2,y=0 area

y = - x - 1, x = - 1, x = 2, y = 0

integral from 0 to pi of x^2sin(2x)

\int_{0}^{π} x^{2} sin (2 x) d x

Frequently Asked Questions (FAQ)

What is the solution for y^{''}+y^'=e^x ?
The solution for y^{''}+y^'=e^x is y=c_{1}+c_{2}e^{-x}+1/2 e^x