What is the solution for y^{''}-36y=-42e^{-5t},y(0)=7,y^'(0)=0 ?

The solution for y^{''}-36y=-42e^{-5t},y(0)=7,y^'(0)=0 is y= 42/11 e^{-5t}+35/11 e^{6t}

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y^{''}-36y=-42e^{-5t},y(0)=7,y^'(0)=0

y^{^{''}} - 36 y = - 42 e^{- 5 t}, y (0) = 7, y^{^{'}} (0) = 0

y = \frac{42}{11} e^{- 5 t} + \frac{35}{11} e^{6 t}

Solution steps

y^{''} (t) - 36 y = - 42 e^{- 5 t}

Solve linear ODE:

y = \frac{42}{11} e^{- 5 t} + \frac{35}{11} e^{6 t}

y = \frac{42}{11} e^{- 5 t} + \frac{35}{11} e^{6 t}

What is the solution for y^{''}-36y=-42e^{-5t},y(0)=7,y^'(0)=0 ?
The solution for y^{''}-36y=-42e^{-5t},y(0)=7,y^'(0)=0 is y= 42/11 e^{-5t}+35/11 e^{6t}