Step-by-step Solution

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Step-by-step explanation

Problem to solve:

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

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

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

Learn how to solve differential equations problems step by step online. Solve the differential equation dy/dx+3/xy=1/(x^2). Multiplying the fraction by y. 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{3}{x} and Q(x)=\frac{1}{x^2}. 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. So the integrating factor \mu(x) is.

$y=\frac{\frac{1}{2}x^2+C_0}{x^3}$
$\frac{dy}{dx}+\frac{3}{x}y=\frac{1}{x^2}$

Main topic:

Differential equations

Time to solve it:

~ 0.09 s (SnapXam)