What is the solution for sqrt(y)dx+(x-8)dy=0,y(9)=36 ?

The solution for sqrt(y)dx+(x-8)dy=0,y(9)=36 is y=(ln^2(x-8))/4-(c_{1}ln(x-8))/2+(c_{1}^2)/4

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sqrt(y)dx+(x-8)dy=0,y(9)=36

y d x + (x - 8) d y = 0, y (9) = 36

y = \frac{ln ^{2} ( x - 8 )}{4} - \frac{c _{1} ln ( x - 8 )}{2} + \frac{c _{1}^{2}}{4}

Solution steps

y d x + (x - 8) d y = 0

Solve separable ODE:

y = \frac{ln ^{2} ( x - 8 )}{4} - \frac{c _{1} ln ( x - 8 )}{2} + \frac{c _{1}^{2}}{4}

y = \frac{ln ^{2} ( x - 8 )}{4} - \frac{c _{1} ln ( x - 8 )}{2} + \frac{c _{1}^{2}}{4}

\int \frac{1}{x ( 1 - x ) ^{2}} d x

\int_{0}^{4} x d x

\frac{d}{d x} (\frac{132}{x ^{13}})

\int_{0}^{\infty} 3 x e^{- 3 x} d x

x \to 0 lim (\frac{csc ( x )}{3 x})

What is the solution for sqrt(y)dx+(x-8)dy=0,y(9)=36 ?
The solution for sqrt(y)dx+(x-8)dy=0,y(9)=36 is y=(ln^2(x-8))/4-(c_{1}ln(x-8))/2+(c_{1}^2)/4