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Popular >

x^{''}-4x^'+4x=e^t+e^{2t}+1

Solution

x^{^{''}} - 4 x^{^{'}} + 4 x = e^{t} + e^{2 t} + 1

Solution

x = c_{1} e^{2 t} + c_{2} t e^{2 t} + e^{t} + \frac{e ^{2 t} t ^{2}}{2} + \frac{1}{4}

Solution steps

x^{''} (t) - 4 x^{'} (t) + 4 x = e^{t} + e^{2 t} + 1

Solve linear ODE:

x = c_{1} e^{2 t} + c_{2} t e^{2 t} + e^{t} + \frac{e ^{2 t} t ^{2}}{2} + \frac{1}{4}

x = c_{1} e^{2 t} + c_{2} t e^{2 t} + e^{t} + \frac{e ^{2 t} t ^{2}}{2} + \frac{1}{4}

Graph

Popular Examples

(d^2y)/(dx^2)+2(dy)/(dx)+10y=2cos(6x)

\frac{d ^{2} y}{d x ^{2}} + 2 \frac{d y}{d x} + 10 y = 2 cos (6 x)

y^{''}+25y=sec^3(5x)

y^{^{''}} + 25 y = sec^{3} (5 x)

y^{''}-3y^'+2y=sin(3x),y(0)=1,y^'(0)=0

y^{^{''}} - 3 y^{^{'}} + 2 y = sin (3 x), y (0) = 1, y^{^{'}} (0) = 0

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

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

y^{''}-4y=96x^2e^{2x}+4e^{-2x}

y^{^{''}} - 4 y = 96 x^{2} e^{2 x} + 4 e^{- 2 x}

Frequently Asked Questions (FAQ)

What is the solution for x^{''}-4x^'+4x=e^t+e^{2t}+1 ?
The solution for x^{''}-4x^'+4x=e^t+e^{2t}+1 is x=c_{1}e^{2t}+c_{2}te^{2t}+e^t+(e^{2t}t^2)/2+1/4