What is the solution for sqrt(y)dx+(x-1)dy=0,y(2)=25 ?

The solution for sqrt(y)dx+(x-1)dy=0,y(2)=25 is y=(ln^2(x-1))/4-(c_{1}ln(x-1))/2+(c_{1}^2)/4

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sqrt(y)dx+(x-1)dy=0,y(2)=25

y d x + (x - 1) d y = 0, y (2) = 25

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

Solution steps

y d x + (x - 1) d y = 0

Solve separable ODE:

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

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

2 y y^{^{'}} = 18 t^{2}, y (0) = 7

\frac{d y}{d t} + 2 y = 5, y (0) = 1

\frac{d y}{d x} = \frac{3 x + x y ^{2}}{2 y + x ^{2} y}, y (2) = 1

\frac{d y}{d x} = 800 y

1 - x^{2} d y - x y d x = 0, y (1) = 2

What is the solution for sqrt(y)dx+(x-1)dy=0,y(2)=25 ?
The solution for sqrt(y)dx+(x-1)dy=0,y(2)=25 is y=(ln^2(x-1))/4-(c_{1}ln(x-1))/2+(c_{1}^2)/4