A) \[y{{e}^{{{x}^{2}}}}=c{{x}^{2}}\]
B) \[y{{e}^{-{{x}^{2}}}}=c{{x}^{2}}\]
C) \[{{y}^{2}}{{e}^{{{x}^{2}}}}=c{{x}^{2}}\]
D) \[{{y}^{2}}{{e}^{-{{x}^{2}}}}=c{{x}^{2}}\]
Correct Answer: C
Solution :
Given equation can be written as \[\left( \frac{1-{{x}^{2}}}{x} \right)dx=\frac{dy}{y}\] After integration, we get \[\log x-\frac{{{x}^{2}}}{2}=\log y+\log c\] Þ \[\log {{x}^{2}}-\log {{y}^{2}}+\log c={{x}^{2}}\]Þ\[\log \frac{c{{x}^{2}}}{{{y}^{2}}}={{x}^{2}}\] Þ \[\frac{c{{x}^{2}}}{{{y}^{2}}}={{e}^{x}}^{2}\]Þ\[c{{x}^{2}}={{y}^{2}}{{e}^{{{x}^{2}}}}\].
You need to login to perform this action.
You will be redirected in
3 sec
