What is the solution for y^{''}+3y^'=0,y(0)=-2,y^'(0)=-(-3) ?

The solution for y^{''}+3y^'=0,y(0)=-2,y^'(0)=-(-3) is y=-e^{-3t}-1

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y^{''}+3y^'=0,y(0)=-2,y^'(0)=-(-3)

y^{^{''}} + 3 y^{^{'}} = 0, y (0) = - 2, y^{^{'}} (0) = - (- 3)

y = - e^{- 3 t} - 1

Solution steps

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

Solve linear ODE:

y = - e^{- 3 t} - 1

y = - e^{- 3 t} - 1

10 x^{^{''}} + 200 x = 0

y^{^{''}} + 2 y^{^{'}} + y = 0, y (0) = 5, y^{^{'}} (0) = - 3

5 y^{^{''}} + 2 y^{^{'}} + 7 y = 0

3 y^{^{''}} + 8 y^{^{'}} + 3 y = 0

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

What is the solution for y^{''}+3y^'=0,y(0)=-2,y^'(0)=-(-3) ?
The solution for y^{''}+3y^'=0,y(0)=-2,y^'(0)=-(-3) is y=-e^{-3t}-1