Solving Linear First-Order Differential Equation y'

Math Problem Statement

y′−y/x=xcosx,

The given first-order differential equation is:

$y' - \frac{y}{x} = x \cos x$

This is a linear first-order differential equation, and it can be solved using an integrating factor.

Rearrange the equation in standard linear form: $y' + P(x)y = Q(x)$ Here, we have: $P(x) = -\frac{1}{x} \quad \text{and} \quad Q(x) = x \cos x$
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Differential Equations
Linear First-Order Equations
Integrating Factor

Standard form of a linear first-order differential equation: y' + P(x)y = Q(x)
Integrating factor: e^(∫P(x) dx)

Theory of Linear First-Order Differential Equations

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