The integrating factor of x frac{dy}{dx} + 3y | vedclass

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Question

(A) The given linear differential equation is $x \frac{dy}{dx} + 3y = x^2$. Dividing both sides by $x$,we get: $\frac{dy}{dx} + \frac{3}{x} y = x$. Co

Vedclass · Accepted Answer

$x^3$

Vedclass · Answer

(A) The given linear differential equation is $x \frac{dy}{dx} + 3y = x^2$. Dividing both sides by $x$,we get: $\frac{dy}{dx} + \frac{3}{x} y = x$. Comparing this with the standard form $\frac{dy}{dx} + Py = Q$,we identify $P = \frac{3}{x}$. The integrating factor $(IF)$ is given by $IF = e^{\int P dx}$. $IF = e^{\int \frac{3}{x} dx} = e^{3 \ln x} = e^{\ln x^3} = x^3$. Thus,the integrating factor is $x^3$.

The integrating factor of $x \frac{dy}{dx} + 3y = x^2$ is

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