What is the solution for (dy)/(dx)=(10+16x)/(xy^2),y=4,x=1 ?

The solution for (dy)/(dx)=(10+16x)/(xy^2),y=4,x=1 is y=\sqrt[3]{30ln(x)+48x+16}

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(dy)/(dx)=(10+16x)/(xy^2),y=4,x=1

\frac{d y}{d x} = \frac{10 + 16 x}{x y ^{2}}, y = 4, x = 1

y = 3 30 ln (x) + 48 x + 16

Solution steps

\frac{d y}{d x} = \frac{10 + 16 x}{x y ^{2}}

Solve separable ODE:

y = 3 30 ln (x) + 48 x + 16

y = 3 30 ln (x) + 48 x + 16

y^{2} + y - x \frac{d y}{d x} = 0

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

\frac{y - 1}{5 + x ^{2}} d y = y^{2} d x

y^{^{'}} = 7 x y

R = \frac{d R}{d t}

What is the solution for (dy)/(dx)=(10+16x)/(xy^2),y=4,x=1 ?
The solution for (dy)/(dx)=(10+16x)/(xy^2),y=4,x=1 is y=\sqrt[3]{30ln(x)+48x+16}