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Home  >>  CBSE XII  >>  Math  >>  Differential Equations
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Which of the following differential equations has $y = x$ as one of its particular solution?

\begin{array}{1 1}(A)\;\frac{d^2y}{dx^2}-x^2\frac{dy}{dx}+xy=x\qquad(B)\;\frac{d^2y}{dx^2}+x\frac{dy}{dx}+xy=x\\(C)\;\frac{d^2y}{dx^2}-x^2\frac{dy}{dx}+xy=0\qquad(D)\;\frac{d^2y}{dx^2}+x\frac{dy}{dx}+xy=0\end{array}

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  • Derivative of $y$ is $y'$ and derivative of $y'$ is $y''$
Step 1:
Given : $y = x$
differentiating this we get
$y' = 1$
Again differentiating this we get,
$y'' = 0$
Step 2:
Substituting for $y'$ and $y''$ and $y$ in the given options we see in the option C
LHS is $y'' - x^2 y' + xy$
On substituting for $y''$ and $y$ we get
$0 - x^2.1 + x^2 = 0$
Hence option C satisfies as the solution
Hence option C is the correct answer.
answered Aug 15, 2013 by sreemathi.v

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