Final Answer
$y=\sin\left(\frac{1}{2}x^2+C_0\right)$
Got another answer? Verify it here!
Step-by-step Solution
Specify the solving method
1
Group the terms of the differential equation. Move the terms of the $y$ variable to the left side, and the terms of the $x$ variable to the right side of the equality
$\frac{1}{\sqrt{1-y^2}}dy=x\cdot dx$
2
Integrate both sides of the differential equation, the left side with respect to
$\int\frac{1}{\sqrt{1-y^2}}dy=\int xdx$
3
Solve the integral $\int\frac{1}{\sqrt{1-y^2}}dy$ and replace the result in the differential equation
$\arcsin\left(y\right)=\int xdx$
4
Solve the integral $\int xdx$ and replace the result in the differential equation
$\arcsin\left(y\right)=\frac{1}{2}x^2+C_0$
5
Find the explicit solution to the differential equation. We need to isolate the variable $y$
$y=\sin\left(\frac{1}{2}x^2+C_0\right)$
Final Answer
$y=\sin\left(\frac{1}{2}x^2+C_0\right)$