A) \[y{{\sin }^{2}}x={{x}^{3}}+c\]
B) \[y\sin x=c\]
C) \[y\cos {{x}^{2}}=c\]
D) \[y\sin {{x}^{2}}=c\]
Correct Answer: A
Solution :
\[\frac{dy}{dx}+2\cot x.y=3{{x}^{2}}\text{cose}{{\text{c}}^{2}}x\] 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.)=\[\int_{{}}^{{}}{Q(\text{I}\text{.F}\text{.})\text{ }dx}\] \[y.{{\sin }^{2}}x=\int_{{}}^{{}}{3{{x}^{2}}\text{cose}{{\text{c}}^{2}}x.{{\sin }^{2}}xdx={{x}^{3}}+c}\].
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