What is the solution for (dy)/(dx)=((1+x))/(xy) ?

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

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(dy)/(dx)=((1+x))/(xy)

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

y = 2 ln (x) + 2 x + c_{1}, y = - 2 ln (x) + 2 x + c_{1}

Solution steps

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

Solve separable ODE:

y = 2 ln (x) + 2 x + c_{1}, y = - 2 ln (x) + 2 x + c_{1}

y = 2 ln (x) + 2 x + c_{1}, y = - 2 ln (x) + 2 x + c_{1}

y^{^{'}} + 5 x^{4} y = x^{4}, y (0) = y^{0}

d x = x^{5} y d y

y^{^{'}} = 1 + x + y^{2} + y^{2} x

\frac{d x}{d t} = 5000 + 0.04 x, x = 18000, t = 0

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