COMPASSLearning

Talk to us Register Login

CBSE Class 12 · 2007 · Differential EquationsLong Answer

Form the differential equation of the family of curves

y = A cos 2 x + B sin 2 x

, where

A

and

B

are constants.

Answer: $\frac{d ^{2} y}{d x ^{2}} + 4 y = 0$

Solution

Two constants

(A, B)

, differentiate twice.

y^{'} = - 2 A sin 2 x + 2 B cos 2 x

y^{''} = - 4 A cos 2 x - 4 B sin 2 x = - 4 (A cos 2 x + B sin 2 x) = - 4 y

\frac{d ^{2} y}{d x ^{2}} + 4 y = 0

CBSE Class 12 Board · 2007 · Subjective

Practise more: all CBSE board PYQs on Differential Equations →

More board questions on Differential Equations

(a) Find the particular solution of the differential equation
$\frac{d y}{d x} - 2 x y = 3 x^{2} e^{x^{2}}; y (0) = 5$

OR
(b) Solve the following differential equation:
$x^{2} d y + y (x + y) d x = 0$
CBSE 2024View solution →
If $\frac{d}{d x} f (x) = 2 x + \frac{3}{x}$ and $f (1) = 1$ , then $f (x)$ is:
CBSE 2023View solution →
Degree of the differential equation $sin x + cos (\frac{d y}{d x}) = y^{2}$ is:
CBSE 2023View solution →
The integrating factor of the differential equation $(1 - y^{2}) \frac{d x}{d y} + y x = a y, (- 1 < y < 1)$ is:
CBSE 2023View solution →
Find the general solution of the differential equation: $(x y - x^{2}) d y = y^{2} d x$
CBSE 2023View solution →
Find the general solution of the differential equation: $(x^{2} + 1) \frac{d y}{d x} + 2 x y = x^{2} + 4$
CBSE 2023View solution →