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Popular >

y^{''}+y^'=x+1

Solution

y^{^{''}} + y^{^{'}} = x + 1

Solution

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

Solution steps

y^{''} (x) + y^{'} (x) = x + 1

Solve linear ODE:

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

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

Graph

Popular Examples

y^{''}-8y^'+7y=x

y^{^{''}} - 8 y^{^{'}} + 7 y = x

2y^{'''}-6y^{''}=x^2

2 y^{^{'''}} - 6 y^{^{''}} = x^{2}

2y^{''}+4y^'+7y=x^2

2 y^{^{''}} + 4 y^{^{'}} + 7 y = x^{2}

y^{''}+4y^'=16x

y^{^{''}} + 4 y^{^{'}} = 16 x

y^{'''}-y^{''}-25y^'+25y=3-e^x+e^{5x}

y^{^{'''}} - y^{^{''}} - 25 y^{^{'}} + 25 y = 3 - e^{x} + e^{5 x}

Frequently Asked Questions (FAQ)

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