dy/dx=xy^2 Solve the Differential Equation

The general solution of the differential equation dy/dx = xy² is given by y=-2/(x²+2K) where K is an arbitrary constant. Here we will learn how to find the general solution of the differential equation.

Set C=2K.

Answer: the solution of $\dfrac{dy}{dx}=xy^2$ is given by y = $-\dfrac{2}{x^2+C}$.

Solve dy/dx=xy²

Given $\dfrac{dy}{dx}=xy^2$

To solve it, we will use the separation of variable method, that is, will separate the variables x and y. By doing so, we get that

$\dfrac{dy}{y^2}=x ~dx$

Integrating, $\int \dfrac{dy}{y^2}= \int x ~dx + K$, where K is a constant.

$\int y^{-2}dy= \int x ~dx + K$

⇒ $\dfrac{y^{-2+1}}{-2+1}=\dfrac{x^2}{2}+K$

⇒ $-\dfrac{1}{y}=\dfrac{x^2}{2}+K$

⇒ $y=-\dfrac{2}{x^2+2K}$

⇒ $y=-\dfrac{2}{x^2+C}$ where C=2K.

So the general solution of dy/dx = xy² is given by y=-2/(x²+C) where C denotes an arbitrary constant of integrals.

Also Read: Solve dy/dx =y/x

Solve dy/dx =sin(x+y)

How to solve dy/dx=x+y

How to Solve dy/dx=x²y

$\dfrac{dy}{dx}=x^2y$

Separating the variables, we get that

$\dfrac{dy}{y}=x^2~dx$

Integrating, $\int \dfrac{dy}{y}=\int x^2~dx+C$

⇒ $\ln |y|=\dfrac{x^3}{3}+C$.

So the solution of dy/dx=x²y is given by ln|y| = x³/3 +C where C is a constant.

Also Read: Solve dy/dx = cos(x+y)

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