Differential Equations Question 79
Question: The solution of the differential equation $ \frac{dy}{dx}+2y\cot x=3x^{2}cose{c^{2}}x $ is
Options:
A) $ y{{\sin }^{2}}x=x^{3}+c $
B) $ y\sin x=c $
C) $ y\cos x^{2}=c $
D) $ y\sin x^{2}=c $
Show Answer
Answer:
Correct Answer: A
Solution:
$ \frac{dy}{dx}+2\cot x.y=3x^{2}cose{c^{2}}x $
This is a linear differential equation in y. I.F. $ ={e^{2\int _{{}}^{{}}{\cot xdx}}}={e^{2\log \sin x}}={{\sin }^{2}}x $
y. (I.F.)= $ \int _{{}}^{{}}{Q(I\text{.F}\text{.})dx} $
$ y.{{\sin }^{2}}x=\int _{{}}^{{}}{3x^{2}cose{c^{2}}x.{{\sin }^{2}}xdx=x^{3}+c} $ .
BETA
