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Popular >

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

Solution

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

Solution

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

Solution steps

y^{''} (x) - y = x^{2}

Solve linear ODE:

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

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

Popular Examples

y^{''}+y=2,y(0)=2,y^'(0)=3

y^{^{''}} + y = 2, y (0) = 2, y^{^{'}} (0) = 3

y^{''}-y=(4e^{-x})/(1-e^{-2x)}

y^{^{''}} - y = \frac{4 e ^{- x}}{1 - e ^{- 2 x}}

y^{''}-2y^'+y=x^{1/3}e^x

y^{^{''}} - 2 y^{^{'}} + y = x^{\frac{1}{3}} e^{x}

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

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

y^{''}+4y=4t,y(0)=1,y^'(0)=5

y^{^{''}} + 4 y = 4 t, y (0) = 1, y^{^{'}} (0) = 5

Frequently Asked Questions (FAQ)

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