A) \[{{(x+y)}^{2}}=\frac{{{a}^{2}}}{2}x+c\]
B) \[{{(x+y)}^{2}}={{a}^{2}}x+c\]
C) \[{{(x+y)}^{2}}=2{{a}^{2}}x+c\]
D) None of these
Correct Answer: D
Solution :
Put \[x+y=v\] Þ \[1+\frac{dy}{dx}=\frac{dv}{dx}\] Þ \[\frac{dy}{dx}=\frac{dv}{dx}-1\] \ \[{{v}^{2}}\left( \frac{dv}{dx}-1 \right)={{a}^{2}}\] Þ \[\frac{dv}{dx}=\frac{{{a}^{2}}}{{{v}^{2}}}+1=\frac{{{a}^{2}}+{{v}^{2}}}{{{v}^{2}}}\] Þ \[\frac{{{v}^{2}}}{{{a}^{2}}+{{v}^{2}}}dv=dx\] Þ \[\left( 1-\frac{{{a}^{2}}}{{{a}^{2}}+{{v}^{2}}} \right)dv=dx\] Þ \[v-a{{\tan }^{-1}}\frac{v}{a}=x+c\] Þ \[y=a{{\tan }^{-1}}\left( \frac{x+y}{a} \right)\]+ c.
You need to login to perform this action.
You will be redirected in
3 sec
