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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

\frac{d ^{2} y}{d x ^{2}} + \frac{d}{d x} (8 y) + 65 y = 100

y^{^{''}} + 2 y^{^{'}} - 15 y = - 5 x^{2} + 3 x - 3

a y^{^{''}} + b y = c

y^{^{''}} + 2 y^{^{'}} + 37 y = 4 H (t)

5 y^{^{''}} + 4 y^{^{'}} + 8 y = 4 x - 1

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