Question: Solve the differential equation dydx = x2y.

A ) y² = 2x³ + C₁
B ) y = 2 / 3x³ + C₁
C ) y² = 2 / 3x³ + C₁
D ) y = x² + C₁
E ) ln y = 1x + C₁

Steps to derive

1 dydx = x2y
 [Write the differential equation.]

2 y dy = x² dx
 [Seperate the variables.]

3 ∫y dy = ∫x² dx
 [Integrate on both sides.]

4 y22 = x33 + C

5 y² = 2 / 3x³ + 2C = 2 / 3x³ + C₁, where C₁ = 2C

6 So, the general solution of the differential equation is y² = 2 / 3x³ + C₁



Hence the right answer is Option C

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