What is the solution for y^{'''}+5y^{''}+4y^'-10y=0 ?

The solution for y^{'''}+5y^{''}+4y^'-10y=0 is y=c_{1}e^t+e^{-3t}(c_{2}cos(t)+c_{3}sin(t))

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y^{'''}+5y^{''}+4y^'-10y=0

y^{^{'''}} + 5 y^{^{''}} + 4 y^{^{'}} - 10 y = 0

y = c_{1} e^{t} + e^{- 3 t} (c_{2} cos (t) + c_{3} sin (t))

Solution steps

y^{'''} (t) + 5 y^{''} (t) + 4 y^{'} (t) - 10 y = 0

Solve linear ODE:

y = c_{1} e^{t} + e^{- 3 t} (c_{2} cos (t) + c_{3} sin (t))

y = c_{1} e^{t} + e^{- 3 t} (c_{2} cos (t) + c_{3} sin (t))

\int \frac{1}{t 9 + 4 t ^{2}} d t

\int \frac{1 - x}{x} d x

\frac{10 lo g _{4} ( t )}{t}

\frac{\partial}{\partial x} (x^{2} sin (x y))

n = 0 \sum \infty 9^{n} x^{n}

What is the solution for y^{'''}+5y^{''}+4y^'-10y=0 ?
The solution for y^{'''}+5y^{''}+4y^'-10y=0 is y=c_{1}e^t+e^{-3t}(c_{2}cos(t)+c_{3}sin(t))