A) \[y=c{{x}^{-3}}-\frac{{{x}^{2}}}{4}\]
B) \[y=c{{x}^{3}}-\frac{{{x}^{2}}}{4}\]
C) \[y=c{{x}^{2}}+\frac{{{x}^{3}}}{5}\]
D) \[y=c{{x}^{-2}}+\frac{{{x}^{3}}}{5}\]
Correct Answer: D
Solution :
Given differential equation is\[\frac{dy}{dx}+\frac{2}{x}.y={{x}^{2}}\] This is of the linear form. \[\therefore \]\[P=\frac{2}{x},Q={{x}^{2}}\] \[I.F={{e}^{\int_{{}}^{{}}{\frac{2}{x}dx}}}={{e}^{\log {{x}^{2}}={{x}^{2}}}}\] Solution is\[y.{{x}^{2}}=\int_{{}}^{{}}{{{x}^{2}}.{{x}^{2}}dx+c=\frac{{{x}^{5}}}{5}+c}\] \[y=\frac{{{x}^{3}}}{5}+c{{x}^{-2}}\]
You need to login to perform this action.
You will be redirected in
3 sec
