Exercise
$\frac{dy}{dx}=\frac{xy+2x-y-2}{x\left(y^2-4\right)}$
Step-by-step Solution
Learn how to solve problems step by step online. Solve the differential equation dy/dx=(xy+2x-y+-2)/(x(y^2-4)). Simplify \sqrt{y^2} using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals 2 and n equals \frac{1}{2}. Calculate the power \sqrt{4}. Simplify \sqrt{y^2} using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals 2 and n equals \frac{1}{2}. Calculate the power \sqrt{4}.
Solve the differential equation dy/dx=(xy+2x-y+-2)/(x(y^2-4))
Final answer to the exercise
$y=2+\sqrt{2x-2\ln\left(x\right)+C_1+4},\:y=2-\sqrt{2x-2\ln\left(x\right)+C_1+4}$