What is the solution for y^{''}+3y^'-10=0,y(0)=1,y^'(0)=9 ?

The solution for y^{''}+3y^'-10=0,y(0)=1,y^'(0)=9 is y=1+17/9-17/9 e^{-3t}+(10t)/3

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y^{''}+3y^'-10=0,y(0)=1,y^'(0)=9

y^{^{''}} + 3 y^{^{'}} - 10 = 0, y (0) = 1, y^{^{'}} (0) = 9

y = 1 + \frac{17}{9} - \frac{17}{9} e^{- 3 t} + \frac{10 t}{3}

Solution steps

y^{''} (t) + 3 y^{'} (t) - 10 = 0

Solve linear ODE:

y = 1 + \frac{17}{9} - \frac{17}{9} e^{- 3 t} + \frac{10 t}{3}

y = 1 + \frac{17}{9} - \frac{17}{9} e^{- 3 t} + \frac{10 t}{3}

y^{^{''}} + y^{^{'}} - 12 y = e^{2 x}

y^{^{''}} + 4 y^{^{'}} + 50 y = 65 cos (2 t)

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

\frac{1}{4} y^{^{''}} + 16 y = 8 sin (8 t)

y^{^{''}} - 9 y = sin (x) + 2 cos (x)

What is the solution for y^{''}+3y^'-10=0,y(0)=1,y^'(0)=9 ?
The solution for y^{''}+3y^'-10=0,y(0)=1,y^'(0)=9 is y=1+17/9-17/9 e^{-3t}+(10t)/3