What is the solution for 25y^{''}-30y^'+9y=0,y^1(0)=e^3 x/5 ?

The solution for 25y^{''}-30y^'+9y=0,y^1(0)=e^3 x/5 is y=c_{1}e^{(3x)/5}+c_{2}e^{(3x)/5}x

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25y^{''}-30y^'+9y=0,y^1(0)=e^3 x/5

25 y^{^{''}} - 30 y^{^{'}} + 9 y = 0, y^{1} (0) = e^{3} \frac{x}{5}

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

Solution steps

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

Solve linear ODE:

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

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

What is the solution for 25y^{''}-30y^'+9y=0,y^1(0)=e^3 x/5 ?
The solution for 25y^{''}-30y^'+9y=0,y^1(0)=e^3 x/5 is y=c_{1}e^{(3x)/5}+c_{2}e^{(3x)/5}x