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Popular >

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

Solution

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

Solution

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

Solution steps

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

Solve linear ODE:

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

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

Graph

Popular Examples

y^{''}-3y^'+2y=4x+6

y^{^{''}} - 3 y^{^{'}} + 2 y = 4 x + 6

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

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

(d^2y)/(dx^2)+y=sin(x)

\frac{d ^{2} y}{d x ^{2}} + y = sin (x)

y^{''}-16y=48t-24e^{-4t},y(0)=0,y^'(0)=24

y^{^{''}} - 16 y = 48 t - 24 e^{- 4 t}, y (0) = 0, y^{^{'}} (0) = 24

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

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

Frequently Asked Questions (FAQ)

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