The general solution of the differential equation dy dx = x^2 y^2… - Vidyadip

MCQ

The general solution of the differential equation $\frac{{dy}}{{dx}} = \frac{{{x^2}}}{{{y^2}}}$ is

✓
${x^3} - {y^3} = c$
B
${x^3} + {y^3} = c$
C
${x^2} + {y^2} = c$
D
${x^2} - {y^2} = c$

✓

Answer

Correct option: A.

${x^3} - {y^3} = c$

a
(a) We have ${y^2}dy = {x^2}dx$

Integrating, we get ${y^3} - {x^3} = c$ ==> ${x^3} - {y^3} = c$.

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