What is the solution for sqrt(y)dx+(x-6)dy=0,y(7)=9 ?

The solution for sqrt(y)dx+(x-6)dy=0,y(7)=9 is y=(ln^2(x-6))/4-(c_{1}ln(x-6))/2+(c_{1}^2)/4

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sqrt(y)dx+(x-6)dy=0,y(7)=9

y d x + (x - 6) d y = 0, y (7) = 9

y = \frac{ln ^{2} ( x - 6 )}{4} - \frac{c _{1} ln ( x - 6 )}{2} + \frac{c _{1}^{2}}{4}

Solution steps

y d x + (x - 6) d y = 0

Solve separable ODE:

y = \frac{ln ^{2} ( x - 6 )}{4} - \frac{c _{1} ln ( x - 6 )}{2} + \frac{c _{1}^{2}}{4}

y = \frac{ln ^{2} ( x - 6 )}{4} - \frac{c _{1} ln ( x - 6 )}{2} + \frac{c _{1}^{2}}{4}

\frac{d y}{d x} 2 y^{5} = arctan (x) ln (x)

(3 y 2 - t 2 y 5) \frac{d y}{d t} + t 2 y 4 = 0

y^{^{'}} = tan (x) y

\frac{d y}{d x} = e^{9 y} + e^{(4 x + 9 y)}

y^{^{'}} + 4 y = 12, y (0) = 0

What is the solution for sqrt(y)dx+(x-6)dy=0,y(7)=9 ?
The solution for sqrt(y)dx+(x-6)dy=0,y(7)=9 is y=(ln^2(x-6))/4-(c_{1}ln(x-6))/2+(c_{1}^2)/4