Question

Find the solution of differential equation $\frac{dy}{dx}$ = $\frac{yƒ'(x)–y^{2}}{ƒ(x)}$ -

• A. ƒ(x) = y (x – c)
• B. ƒ(x) = y (c – x)
• C. ƒ(x) = y (x + c)
• D. None

Answer 1

Answer: (C)

ƒ(x) = y (x + c)

Answer 2

The given equation is $\frac{dy}{dx}$ = $\frac{yƒ'(x) - y^{2}}{ƒ(x)}$

Ž yƒ¢ (x) dx – ƒ(x) dy = y²dx

Ž $\frac{yƒ'(x)dx - ƒ(x)dy}{y^{2}}$ = dx Ž d $\left\lbrack \frac{ƒ(x)}{y} \right\rbrack$ = dx

On integration, we get

$\frac{ƒ(x)}{y}$ = x + c Ž ƒ(x) = y(x + c)