Question

The solution of differential equation

yy¢= x $\left( \frac{y^{2}}{x^{2}} + \frac{f(y^{2}/x^{2})}{f'(y^{2}/x^{2})} \right)$is

• A. f(y²/x²) = cx²
• B. x²f(y²/x²) =c²y²
• C. x²f(y²/x²)= c
• D. f(y²/x²) = cy/x

Answer 1

Answer: (A)

f(y²/x²) = cx²

Answer 2

Putting y = vx, we get

v $\left\lbrack v + x\frac{dv}{dx} \right\rbrack$ = v²+ $\frac{f(v^{2})}{f'(v^{2})}$

Ž $\frac{2vf'(v^{2})}{f(v^{2})}dv$ = 2 $\frac{dv}{x}$

Now integrating both sides, we get

log f (v²) = log x² + log c

[log c = constant]

or f(y²/x²) = cx²