Exercise
$10x-6y\sqrt{x^2+1}\frac{dy}{dx}=0,y\left(0\right)=-6$
Step-by-step Solution
Learn how to solve problems step by step online. Solve the differential equation 10x-6y(x^2+1)^(1/2)dy/dx=0. Factor 10x-6y\sqrt{x^2+1}\left(\frac{dy}{dx}\right) by the greatest common divisor 2. Divide both sides of the equation by 2. We need to isolate the dependent variable y, we can do that by simultaneously subtracting 5x from both sides of the equation. Divide both sides of the equation by -1.
Solve the differential equation 10x-6y(x^2+1)^(1/2)dy/dx=0
Final answer to the exercise
$y=\frac{\sqrt{\left(-6\sqrt{3}\right)^{2}+10-10\sqrt{x^2+1}}}{\sqrt{3}}$