What is the solution for -4y^{''}+9y=15 ?

The solution for -4y^{''}+9y=15 is y=c_{1}e^{(3t)/2}+c_{2}e^{-(3t)/2}+5/3

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-4y^{''}+9y=15

- 4 y^{^{''}} + 9 y = 15

y = c_{1} e^{\frac{3 t}{2}} + c_{2} e^{- \frac{3 t}{2}} + \frac{5}{3}

Solution steps

- 4 y^{''} (t) + 9 y = 15

Solve linear ODE:

y = c_{1} e^{\frac{3 t}{2}} + c_{2} e^{- \frac{3 t}{2}} + \frac{5}{3}

y = c_{1} e^{\frac{3 t}{2}} + c_{2} e^{- \frac{3 t}{2}} + \frac{5}{3}

y^{^{''}} - 4 y^{^{'}} + 3 y = t^{2} e^{2 t}

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

y^{^{''}} + 2 y^{^{'}} + y = cos (x) + 3 sin (2 x)

y^{^{''}} - y = 4 e^{x}

y^{^{''}} - y = x^{2} e^{x} + e^{3 x}

What is the solution for -4y^{''}+9y=15 ?
The solution for -4y^{''}+9y=15 is y=c_{1}e^{(3t)/2}+c_{2}e^{-(3t)/2}+5/3