The general solution of the differential equa | vedclass

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Question

(A) Given the differential equation: $\frac{dy}{dx} = \frac{x^2}{y^2}$ Using the method of variable separation,we can write: $y^2 dy = x^2 dx$ Integra

Vedclass · Accepted Answer

$x^3 - y^3 = c$

Vedclass · Answer

(A) Given the differential equation: $\frac{dy}{dx} = \frac{x^2}{y^2}$ Using the method of variable separation,we can write: $y^2 dy = x^2 dx$ Integrating both sides: $\int y^2 dy = \int x^2 dx$ This gives: $\frac{y^3}{3} = \frac{x^3}{3} + C_1$ Multiplying by $3$: $y^3 = x^3 + 3C_1$ Rearranging the terms: $x^3 - y^3 = -3C_1$ Let $-3C_1 = c$,where $c$ is an arbitrary constant: $x^3 - y^3 = c$ Thus,the correct option is $A$.

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

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