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Exercise

$dy=\sqrt{1-y^2}dx\frac{1}{2}$

Step-by-step Solution

1

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

$\int1dy=\int\frac{1}{2}dx$
2

Solve the integral $\int1dy$ and replace the result in the differential equation

$y=\int\frac{1}{2}dx$
3

Solve the integral $\int\frac{1}{2}dx$ and replace the result in the differential equation

$y=\frac{1}{2}x+C_0$

Final answer to the exercise

$y=\frac{1}{2}x+C_0$

Try other ways to solve this exercise

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  • Exact Differential Equation
  • Linear Differential Equation
  • Separable Differential Equations
  • Homogeneous Differential Equation
  • Integrate by partial fractions
  • Product of Binomials with Common Term
  • FOIL Method
  • Integrate by substitution
  • Integrate by parts
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Similar Questions Solved

$\frac{dy}{dx}=y^2-9$

$\frac{dy}{dx}=y^2-4$

$\frac{dy}{dx}=y-y^2$

$\frac{dy}{dx}=y\left(y+2\right)$

$\frac{dy}{dx}=\left(1+e^{-x}\right)\left(y^2-1\right)$

$\frac{dy}{dx}=\frac{x}{2x-y}$

$\frac{dy}{dx}=y\left(1-y\right)$

Main Topic: Separable Differential Equations

A separable differential equation is one that can be solved by separating variables, that is, when all expressions involving a variable can be placed on one side of the equation, and expressions involving the other variable on the other side of the equation.

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