Final Answer
$\arcsin\left(y\right)=\sqrt{x}+C_0$
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Step-by-step Solution
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1
Rewrite the differential equation
$\frac{dy}{dx}=\frac{\sqrt{1-y^2}}{2\sqrt{x}}$
Learn how to solve differential equations problems step by step online.
$\frac{dy}{dx}=\frac{\sqrt{1-y^2}}{2\sqrt{x}}$
Learn how to solve differential equations problems step by step online. Solve the differential equation 2x^1/2dy/dx=(1-y^2)^1/2. Rewrite the differential equation. 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. Integrate both sides of the differential equation, the left side with respect to . Solve the integral \int\frac{1}{\sqrt{1-y^2}}dy and replace the result in the differential equation.
Final Answer
$\arcsin\left(y\right)=\sqrt{x}+C_0$