Differential Equations — Class 12 Maths Solution

exemplar objective MCQ NCERT EXEMP.Q.65,Page.200
Question

The differential equation for which $y = a\cos x + b\sin x$ is a

  • (a) $\frac{{{d^2}y}}{{d{x^2}}} + y = 0$ ✓ Correct
  • (b) $\frac{{{d^2}y}}{{d{x^2}}} - y = 0$
  • (c) $\frac{{{d^2}y}}{{d{x^2}}} + (a + b)y = 0$
  • (d) $\frac{{{d^2}y}}{{d{x^2}}} + (a - b)y = 0$
Step-by-step Solution
Correct answer: option (a)

Given that, $y = a\cos x + b\sin x$

On differentiating both sides w.r.t. $x$,

we get

$\frac{{dy}}{{dx}} = - a\sin x + b\cos x$

Again, differentiating w.r.t. $x$,

we get
$\frac{{{d^2}y}}{{d{x^2}}} = - a\sin x + b\cos x$

$\Rightarrow$ $\frac{{{d^2}y}}{{d{x^2}}} = - y$

$\Rightarrow$ $\frac{{{d^2}y}}{{d{x^2}}} + y = 0$

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NCERT & Exemplar solution for CBSE Class 12 Mathematics, Differential Equations. Curated by Sachin Sharma. Free for all students.