Question

The solution of differential equation $\frac{dy}{dx}+y\tan x=2x+x^2\tan x$ is?

• A. $y=x^2+c\cos x$
• B. $y=2x^2-c\cos x$
• C. $y+x^2=c\cos x$
• D. $y+2x^2=c\cos x$

Answer 1

Answer: (A)

$y=x^2+c\cos x$

$\frac{dy}{dx}+\tan x\cdot y=2x+x^2\tan x$
I.F. $=e^{ln\left(\sec x\right)}=\sec x$
$y\sec x=\int (2x+x^2\tan x)\sec xdx+c=I1+c$
$y\sec x=\int 2x\sec xdx+x^2\sec x\tan xdx$
$y\sec x=\int 2x\sec xdx+(x^2\sec x-\int 2x\sec xdx+c)$
$y\sec x=x^2\sec x+c$
$y=x^2+c\cos x$.