The correct answer is (c) 7y^2=2x^3+5
To explain I would say: Given that, \(\frac{dy}{dx}=\frac{3x^2}{7y}\)
Separating the variables, we get
7y dy=3x^2 dx
Integrating both sides, we get
\(7\int y \,dy=3\int x^2 \,dx\)
\(\frac{7y^2}{2}=3(\frac{x^3}{3})+C\)
\(\frac{7y^2}{2}=x^3\)+C –(1)
Given that y=1, when x=1
Substituting the values in equation (1), we get
\(\frac{7(1)^2}{2}=(1)^3+C\)
\(C=\frac{7}{2}-1=\frac{5}{2}\)
Hence, the particular solution of the given differential equation is:
\(\frac{7y^2}{2}=x^3+\frac{5}{2}\)
⇒7y^2=2x^3+5