engineering recuitment AAI ATC Junior Executive 2025 Mock Test Series Mathematics Differential Equations Solution of Differential Equations
The solution of the differential equation \(\frac{{dy}}{{dx}} = \frac{y}{x} + \frac{{f\left( {\frac{y}{x}} \right)}}{{f'\left( {\frac{y}{x}} \right)}}\)is (where C is an arbitrary constant)
1
\(x.f\left( {\frac{y}{x}} \right) = C\)
2
\(f\left( {\frac{y}{x}} \right) = Cx\)
3
\(y.f\left( {\frac{y}{x}} \right) = C\)
4
\(f\left( {\frac{y}{x}} \right) = Cy\)