9. differential equations — ગણિત ધોરણ 12 સાયન્સ — Question

Now integrating factor $(I.F.)$$ = {e^{\int {Pdx} }} = {e^{\int {\tan dx} }}$

$ = {e^{\log \sec x}} = \sec x$

Thus solution is given by, $y.{e^{\int {Pdx} }} = \int Q .\,{e^{\int {Pdx} }}dx + c$

==> $y.\sec x = \int {{x^m}} .\cos x.\sec xdx + c$ ==> $y\sec x = \frac{{{x^{m + 1}}}}{{m + 1}} + c$

==> $(m + 1)y = {x^{m + 1}}\cos x + c(m + 1)\cos x$.