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Popular >

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

Solution

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

Solution

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

Solution steps

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

Solve linear ODE:

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

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

Graph

Popular Examples

9y^{''}-16y=sin(x)

9 y^{^{''}} - 16 y = sin (x)

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

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

y^{''}+25y=3,y(0)=1,y^'(0)=5

y^{^{''}} + 25 y = 3, y (0) = 1, y^{^{'}} (0) = 5

y^{''}+20y^'+200y=400

y^{^{''}} + 20 y^{^{'}} + 200 y = 400

y^{'''}-7y^{''}=x^2+2cos(x)

y^{^{'''}} - 7 y^{^{''}} = x^{2} + 2 cos (x)

Frequently Asked Questions (FAQ)

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