Calculus

Differential Equations

Medium

core

Which of the following differential equations has $y=x$ as one of the particular solution?

$\dfrac{d^2y}{dx^2}-x\dfrac{dy}{dx}+xy=x$

$\dfrac{d^2y}{dx^2}+x\dfrac{dy}{dx}+xy=x$

$\dfrac{d^2y}{dx^2}-x^2\dfrac{dy}{dx}+xy=0$

$\dfrac{d^2y}{dx^2}+x\dfrac{dy}{dx}+xy=0$

✅ Correct Option: 3

For $y=x$ we have $\dfrac{dy}{dx}=1$ and $\dfrac{d^2y}{dx^2}=0$ . Substituting in option 3: $0-x^2(1)+x(x)=0$ , which satisfies the equation. The other three do not reduce to an identity.

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Which of the following differential equations has y=xy=xy=x as one of the particular solution?

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

Which of the following differential equations has $y=x$ as one of the particular solution?