The integrating factor of the differential equation \(\rm \frac{dy}{dx} + xy = x\) is

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Navik GD Mathematics 21 March 2021 (All Shifts) Questions

Answer 1

Concept:

Integrating factor, (IF) for a differential equation, \(\rm\frac{dx}{dy}+Px= Q\), where P and Q are given continuous function of y.

IF = \(\rm e^{\int Pdy}\)

Calculation:

Given differential equation

\(\rm \frac{dy}{dx} + xy = x\)

Now, this differential equation is in the form

\(\rm \frac{dy}{dx} + y P(x) = Q(x)\)

where, P(x) = x and Q(x) = x

Integrating Factor (I.F.) = \(\rm e^{\int P(x)} dx\)

I.F. = \(\rm e^{\int x} dx\) = \(\rm e^{\frac{x^{2}}{2}}\)