Solve the differential equation dx/dy=(a+(-b)/y)^2

 Exercise

$\frac{dx}{dy}=\left(a-\frac{b}{y}\right)^2$

 

Multiply both sides of the equation by $dy$

$dx=\left(a+\frac{-b}{y}\right)^2dy$

 

Integrate both sides of the differential equation, the left side with respect to $y$, and the right side with respect to $x$

$\int1dx=\int\left(a+\frac{-b}{y}\right)^2dy$

 

Solve the integral $\int1dx$ and replace the result in the differential equation

$x=\int\left(a+\frac{-b}{y}\right)^2dy$

 

Solve the integral $\int\left(a+\frac{-b}{y}\right)^2dy$ and replace the result in the differential equation

$x=a^2y-2ba\ln\left|y\right|+\frac{b^2}{-y}+C_0$

$x=a^2y-2ba\ln\left|y\right|+\frac{b^2}{-y}+C_0$

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