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Popular >

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

Solution

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

Solution

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

Solution steps

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

Solve linear ODE:

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

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

Graph

Popular Examples

x^{''}+2x^'+151x=8cos(12t)

x^{^{''}} + 2 x^{^{'}} + 151 x = 8 cos (12 t)

y^{''}+3y=-48t^2e^3t

y^{^{''}} + 3 y = - 48 t^{2} e^{3} t

y^{''''}-256y=2e^{-4x}+3e^{3x}+cos(4x)+2

y^{^{''''}} - 256 y = 2 e^{- 4 x} + 3 e^{3 x} + cos (4 x) + 2

y^{''}+y=3e^{-6x},y(0)=0,y^'(0)=0

y^{^{''}} + y = 3 e^{- 6 x}, y (0) = 0, y^{^{'}} (0) = 0

(D^2-2D+1)y=e^{2x}(e^x+1)^{-2}

(D^{2} - 2 D + 1) y = e^{2 x} (e^{x} + 1)^{- 2}

Frequently Asked Questions (FAQ)

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