What is the solution for 25y^{''}-30y^'+9y=0 ?

The solution for 25y^{''}-30y^'+9y=0 is y=c_{1}e^{(3t)/5}+c_{2}e^{(3t)/5}t

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25y^{''}-30y^'+9y=0

25 y^{^{''}} - 30 y^{^{'}} + 9 y = 0

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

Solution steps

25 y^{''} (t) - 30 y^{'} (t) + 9 y = 0

Solve linear ODE:

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

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

What is the solution for 25y^{''}-30y^'+9y=0 ?
The solution for 25y^{''}-30y^'+9y=0 is y=c_{1}e^{(3t)/5}+c_{2}e^{(3t)/5}t