A) \[y=\frac{{{x}^{2}}+c}{4{{x}^{2}}}\]
B) \[y=\frac{{{x}^{2}}}{4}+c\]
C) \[y=\frac{{{x}^{4}}+c}{{{x}^{2}}}\]
D) \[y=\frac{{{x}^{4}}+c}{4{{x}^{2}}}\]
E) \[y=\frac{{{x}^{3}}}{4}+\frac{c}{{{x}^{2}}}\]
Correct Answer: D
Solution :
\[x=\frac{dy}{dx}+2y={{x}^{2}}\] On differentiating w.r.t\[x,\]we get \[\frac{dy}{dx}+\frac{2}{x}y=x\] Integrating factor\[={{e}^{\int{\frac{2}{x}dx}}}={{x}^{2}}\] \[\therefore \]Required solution is \[y.{{x}^{2}}=\int{{{x}^{3}}}dx=\frac{{{x}^{4}}}{4}+c=\frac{{{x}^{4}}+c}{4}\] \[\therefore \] \[y=\frac{{{x}^{4}}+c}{4{{x}^{2}}}\]
You need to login to perform this action.
You will be redirected in
3 sec
