Given, \(\frac{dy}{dx}\) + y tan x = 3x2 + x3 tan x
⇒ \(\frac{dy}{dx}\) + tan x. y = 3x2 + x3 tan x
Comparing the given differential equation with linear from
\(\frac{dy}{dx} \) + Py = Q, we get
P = tan x, Q = 3x2 + x3 tan x.
\(\therefore\) IF = e∫tan x dx = elog sec x = sec x.
Therefore, general solution is given by
Hence required particular solution is
y = x3 - \(\frac{2\pi^3}{27}\) cos x.