Question

Solution of the equation (xy⁴ + y) dx – x dy = 0 is –

• A. 4x⁴y³ + 3x³ = cy³
• B. 3x³y⁴ + 4y³ = cx³
• C. 3x⁴y³ + 4x³ = cy³
• D. None of these

Answer 1

Answer: (C)

3x⁴y³ + 4x³ = cy³

Answer 2

We have, xy⁴ dx + y dx – x dy = 0

Ž x dx + $\frac{ydx - xdy}{y^{4}}$ = 0

Ž x³ dx + $\left( \frac{x}{y} \right)^{2}$ . $\frac{ydx - xdy}{y^{2}}$= 0

Ž x³ dx + $\left( \frac{x}{y} \right)^{2}$d $\left( \frac{x}{y} \right)$ = 0

Integrating, we get $\frac{x^{4}}{4}$ + $\frac{1}{3}$ $\left( \frac{x}{y} \right)^{3}$ = c

Ž 3x⁴y³ + 4x³ = cy³,

Which is the required solution.