What is the solution for sqrt(y)dx+(x-9)dy=0,y(10)=49 ?

The solution for sqrt(y)dx+(x-9)dy=0,y(10)=49 is y=(ln^2(x-9))/4-(c_{1}ln(x-9))/2+(c_{1}^2)/4

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sqrt(y)dx+(x-9)dy=0,y(10)=49

y d x + (x - 9) d y = 0, y (10) = 49

y = \frac{ln ^{2} ( x - 9 )}{4} - \frac{c _{1} ln ( x - 9 )}{2} + \frac{c _{1}^{2}}{4}

Solution steps

y d x + (x - 9) d y = 0

Solve separable ODE:

y = \frac{ln ^{2} ( x - 9 )}{4} - \frac{c _{1} ln ( x - 9 )}{2} + \frac{c _{1}^{2}}{4}

y = \frac{ln ^{2} ( x - 9 )}{4} - \frac{c _{1} ln ( x - 9 )}{2} + \frac{c _{1}^{2}}{4}

\frac{d y}{d t} = 12 - \frac{y}{50}

v y ln (v) d y - y (v d y + y d v) = 0

y^{^{'}} = 0.01398 y, y (0) = 150

\frac{d y}{d x} = (- 2 x + 1) y, y (0) = 6.8

\frac{d y}{d x} + y = y (sin (x) + 1)

What is the solution for sqrt(y)dx+(x-9)dy=0,y(10)=49 ?
The solution for sqrt(y)dx+(x-9)dy=0,y(10)=49 is y=(ln^2(x-9))/4-(c_{1}ln(x-9))/2+(c_{1}^2)/4