What is the solution for (x^2-20x+51)(dy)/(dx)=y ?

The solution for (x^2-20x+51)(dy)/(dx)=y is y=(c_{1}\sqrt[14]{x-17})/(\sqrt[14]{x-3)}

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(x^2-20x+51)(dy)/(dx)=y

(x^{2} - 20 x + 51) \frac{d y}{d x} = y

y = \frac{c _{1} 14 x - 17}{14 x - 3}

Solution steps

(x^{2} - 20 x + 51) \frac{d y}{d x} = y

Solve separable ODE:

y = \frac{c _{1} 14 x - 17}{14 x - 3}

y = \frac{c _{1} 14 x - 17}{14 x - 3}

\frac{d y}{d x} = \frac{( e ^{y} \cdot sin ^{2} ( x ) )}{y \cdot sec ( x )}

7 \frac{d y}{d x} + x^{2} y = 0

4 y^{^{'}} + 2 x + 2 c e^{2 y} y^{^{'}} = 0

\frac{d}{d x} (x y - 1) = 0

4 y^{^{'}} - 6 y^{^{'}} + 7 y = 0

What is the solution for (x^2-20x+51)(dy)/(dx)=y ?
The solution for (x^2-20x+51)(dy)/(dx)=y is y=(c_{1}\sqrt[14]{x-17})/(\sqrt[14]{x-3)}