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

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

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sqrt(y)dx+(1+x)dy=0

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

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

Solution steps

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

Solve separable ODE:

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

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

\frac{\partial}{\partial x} (\frac{x ^{2} + y ^{2} - 7}{x y})

\frac{d x}{d t} + 3 t^{3} x^{5} + \frac{x}{t} = 0

x^{2} + 8 x - 2

x^{2} d y + 2 x y d x = 0

\frac{d ^{2}}{d x ^{2}} (- cos (x) ln (sec (x) + tan (x)))

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