A) \[{{x}^{3}}-{{y}^{3}}=12x+c'\]
B) \[{{x}^{3}}+{{y}^{3}}=12x+c'\]
C) \[{{y}^{3}}+{{x}^{3}}=12x+c'\]
D) None of these
Correct Answer: B
Solution :
[b] \[\because {{x}^{2}}+{{y}^{2}}\frac{dy}{dx}=4\] \[\Rightarrow {{y}^{2}}\frac{dy}{dx}=\left( 4-{{x}^{2}} \right)\] Integrating, we have \[\int{{{y}^{2}}.dy}=\int{(4-{{x}^{2}})}.dy\] \[\Rightarrow \frac{{{y}^{3}}}{3}=4x-\frac{{{x}^{3}}}{3}+c\] \[\Rightarrow {{y}^{3}}+{{x}^{3}}=12x+c'\] Hence, option [b] is the required solution.
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