The differential equation of 3 y=[3]{x+c} is

Correct Answer is : dydx=181y2d y/d x={1}{81 y²}dxdy=81y21

Correct Answer is : dydx=181y2d y/d x={1}{81 y²}dxdy=81y21

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MHTCET 13 Apr 2026 Shift 2 Paper

Question : 135 of 150

Marks: +1, -0

3 y=\sqrt[3]{x+c}

Solution:

Concept:

To form the differential equation, eliminate the arbitrary constant

c

by differentiating the given equation.

Explanation:

Given:

3y = \sqrt[3]{x+c}

Cubing both sides removes the cube root:

(3y)^3 = x+c

27y^3 = x+c

Differentiate both sides with respect to

x

\frac{d}{dx}(27y^3) = \frac{d}{dx}(x+c)

Using the chain rule:

81y^2 \frac{dy}{dx} = 1

Therefore,

\frac{dy}{dx} = \frac{1}{81y^2}

Answer:

The differential equation is

\frac{dy}{dx} = \frac{1}{81y^2}

, which matches Option C.

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