The Integrating Factor of the differential equation x dx - y = 2 x 2 is e - x e - y x x

option c is correct The given equation can be written as dx - x = 2x which is a linear equation of type dx + Py = Q Where, P = - x ,Q = 2x = e P dx = e x dx = e - x = e = x - 1 = x

Differential Equations — Class 12 Maths Solution

ncert exercise SA NCERT Ex.9.6,Q.18,Page 413

Question

The Integrating Factor of the differential equation $x\cfrac{{dy}}{{dx}} - y = 2{x^2}$ is

• ${e^{ - x}}$

• ${e^{ - y}}$

• $\cfrac{1}{x}$

• $x$

Step-by-step Solution

option c is correct

The given equation can be written as $\cfrac{{dy}}{{dx}} - \cfrac{y}{x} = 2x$

which is a linear equation of type $\cfrac{{dy}}{{dx}} + Py = Q$

Where, $P = - \cfrac{1}{x},Q = 2x$

$\therefore$ ${\rm{I}}{\rm{.F}}{\rm{.}} = {e^{\int P dx}} = {e^{\int { - \cfrac{1}{x}dx} }} = {e^{ - \log x}} = {e^{\log {x^{ - 1}}}} = {x^{ - 1}} = \cfrac{1}{x}$

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