(A) Given the differential equation: $x^2 + y^2 \frac{dy}{dx} = 4$.Rearranging the terms to separate the variables,we get:$y^2 dy = (4 - x^2) dx$.Now,

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(A) Given the differential equation: $x^2 + y^2 \frac{dy}{dx} = 4$.Rearranging the terms to separate the variables,we get:$y^2 dy = (4 - x^2) dx$.Now,integrate both sides:$\int y^2 dy = \int (4 - x^2) dx$.Performing the integration:$\frac{y^3}{3} = 4x - \frac{x^3}{3} + C_1$.Multiplying the entire equation by $3$:$y^3 = 12x - x^3 + 3C_1$.Let $3C_1 = C$,then:$x^3 + y^3 = 12x + C$.

Class 12 Mathematics Differential Equations Variable separable type differential equations

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The solution of $x^2 + y^2 \frac{dy}{dx} = 4$ is

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A
$x^3 + y^3 = 12x + C$
B
$x^2 + y^2 = 4x + C$
C
$x^3 - y^3 = 12x + C$
D
$x^2 - y^2 = 4x + C$

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