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Popular >

2x^{''}+5x^'+2x=4e^{-2t}-t

Solution

2 x^{^{''}} + 5 x^{^{'}} + 2 x = 4 e^{- 2 t} - t

Solution

x = c_{1} e^{- \frac{t}{2}} + c_{2} e^{- 2 t} - \frac{4 e ^{- 2 t} t}{3} - \frac{t}{2} + \frac{5}{4}

Solution steps

2 x^{''} (t) + 5 x^{'} (t) + 2 x = 4 e^{- 2 t} - t

Solve linear ODE:

x = c_{1} e^{- \frac{t}{2}} + c_{2} e^{- 2 t} - \frac{4 e ^{- 2 t} t}{3} - \frac{t}{2} + \frac{5}{4}

x = c_{1} e^{- \frac{t}{2}} + c_{2} e^{- 2 t} - \frac{4 e ^{- 2 t} t}{3} - \frac{t}{2} + \frac{5}{4}

Graph

Popular Examples

y^{''}-9y=(9t)/(e^{3t)}

y^{^{''}} - 9 y = \frac{9 t}{e ^{3 t}}

(d^2x)/(dt^2)-3(dx)/(dt)+12x=9t

\frac{d ^{2} x}{d t ^{2}} - 3 \frac{d x}{d t} + 12 x = 9 t

y^{''}+y^'+5y=2x

y^{^{''}} + y^{^{'}} + 5 y = 2 x

y^{''}-4y^'+13y=e^{2t}*sin(3t),y(0)=4

y^{^{''}} - 4 y^{^{'}} + 13 y = e^{2 t} \cdot sin (3 t), y (0) = 4

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

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

Frequently Asked Questions (FAQ)

What is the solution for 2x^{''}+5x^'+2x=4e^{-2t}-t ?
The solution for 2x^{''}+5x^'+2x=4e^{-2t}-t is x=c_{1}e^{-t/2}+c_{2}e^{-2t}-(4e^{-2t}t)/3-t/2+5/4