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Popular >

y^{''}+y^'-6y=4te^{2t}

Solution

y^{^{''}} + y^{^{'}} - 6 y = 4 t e^{2 t}

Solution

y = c_{1} e^{2 t} + c_{2} e^{- 3 t} + \frac{2 e ^{2 t} t ^{2}}{5} - \frac{4 e ^{2 t} t}{25}

Solution steps

y^{''} (t) + y^{'} (t) - 6 y = 4 t e^{2 t}

Solve linear ODE:

y = c_{1} e^{2 t} + c_{2} e^{- 3 t} + \frac{2 e ^{2 t} t ^{2}}{5} - \frac{4 e ^{2 t} t}{25}

y = c_{1} e^{2 t} + c_{2} e^{- 3 t} + \frac{2 e ^{2 t} t ^{2}}{5} - \frac{4 e ^{2 t} t}{25}

Graph

Popular Examples

y^{''}-9y=e^{3x},y(0)=3,y^'(0)=10

y^{^{''}} - 9 y = e^{3 x}, y (0) = 3, y^{^{'}} (0) = 10

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

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

(x^{''})/2+10x^'+100x=150

\frac{x ^{^{''}}}{2} + 10 x^{^{'}} + 100 x = 150

y^{''}+ay^'+by=t+e^{3t}

y^{^{''}} + a y^{^{'}} + b y = t + e^{3 t}

(d^2y)/(dt^2)-3(dy)/(dt)-40y=5+4t

\frac{d ^{2} y}{d t ^{2}} - 3 \frac{d y}{d t} - 40 y = 5 + 4 t

Frequently Asked Questions (FAQ)

What is the solution for y^{''}+y^'-6y=4te^{2t} ?
The solution for y^{''}+y^'-6y=4te^{2t} is y=c_{1}e^{2t}+c_{2}e^{-3t}+(2e^{2t}t^2)/5-(4e^{2t}t)/(25)