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Popular >

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

Solution

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

Solution

y = c_{1} + c_{2} e^{- x} + 2 x^{2} - 4 x

Solution steps

y^{''} (x) + y^{'} (x) = 4 x

Solve linear ODE:

y = c_{1} + c_{2} e^{- x} + 2 x^{2} - 4 x

y = c_{1} + c_{2} e^{- x} + 2 x^{2} - 4 x

Graph

Popular Examples

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

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

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

y^{''}-4y^'+3y=9x^2-36x+37

y^{^{''}} - 4 y^{^{'}} + 3 y = 9 x^{2} - 36 x + 37

y^{''}+3y^'=2x^4+x^2e^{-3x}+sin(3x)

y^{^{''}} + 3 y^{^{'}} = 2 x^{4} + x^{2} e^{- 3 x} + sin (3 x)

y^{''}-2y^'+5y=1+t,y(0)=0,y^'(0)=4

y^{^{''}} - 2 y^{^{'}} + 5 y = 1 + t, y (0) = 0, y^{^{'}} (0) = 4

Frequently Asked Questions (FAQ)

What is the solution for y^{''}+y^'=4x ?
The solution for y^{''}+y^'=4x is y=c_{1}+c_{2}e^{-x}+2x^2-4x