What is the solution for (x-4)2y-5(x-4)y^'+9y=0 ?

The solution for (x-4)2y-5(x-4)y^'+9y=0 is y=e^{1/5 (2(x-4)+9ln(x-4))+c_{1}}

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(x-4)2y-5(x-4)y^'+9y=0

(x - 4) 2 y - 5 (x - 4) y^{^{'}} + 9 y = 0

y = e^{\frac{1}{5} (2 (x - 4) + 9 l n (x - 4)) + c_{1}}

Solution steps

(x - 4) 2 y - 5 (x - 4) y^{'} (x) + 9 y = 0

Solve separable ODE:

y = e^{\frac{1}{5} (2 (x - 4) + 9 l n (x - 4)) + c_{1}}

y = e^{\frac{1}{5} (2 (x - 4) + 9 l n (x - 4)) + c_{1}}

What is the solution for (x-4)2y-5(x-4)y^'+9y=0 ?
The solution for (x-4)2y-5(x-4)y^'+9y=0 is y=e^{1/5 (2(x-4)+9ln(x-4))+c_{1}}