** Final answer to the problem

**

** Step-by-step Solution **

** How should I solve this problem?

- Choose an option
- Exact Differential Equation
- Linear Differential Equation
- Separable Differential Equation
- Homogeneous Differential Equation
- Integrate by partial fractions
- Product of Binomials with Common Term
- FOIL Method
- Integrate by substitution
- Integrate by parts
- Load more...

**

**

Divide all the terms of the differential equation by $x^2+1$

Learn how to solve differential equations problems step by step online.

$\frac{x^2+1}{x^2+1}\frac{dy}{dx}+\frac{3xy}{x^2+1}=\frac{6x}{x^2+1}$

Learn how to solve differential equations problems step by step online. Solve the differential equation (x^2+1)dy/dx+3xy=6x. Divide all the terms of the differential equation by x^2+1. Simplifying. We can identify that the differential equation has the form: \frac{dy}{dx} + P(x)\cdot y(x) = Q(x), so we can classify it as a linear first order differential equation, where P(x)=\frac{3x}{x^2+1} and Q(x)=\frac{6x}{x^2+1}. In order to solve the differential equation, the first step is to find the integrating factor \mu(x). To find \mu(x), we first need to calculate \int P(x)dx.

** Final answer to the problem

**