Step-by-step Solution

Solve the differential equation $\frac{dy}{dx}+y\frac{3}{x}=\frac{1}{x^2}$

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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.

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

Unlock this full step-by-step solution!

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.

Final Answer

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

Related formulas:

1. See formulas

Time to solve it:

~ 0.09 s (SnapXam)