If d^2 y d x^2 + x = 0, then solution of the differential equatio… - Vidyadip

MCQ

If $\frac{{{d^2}y}}{{d{x^2}}} + \sin x = 0,$ then solution of the differential equation is.

✓
$\sin x + {c_1}x + {c_2}$
B
$\cos x + {c_1}x + {c_2}$
C
$\tan x + {c_1}x + {c_2}$
D
$\log \sin x + {c_1}x + {c_2}$

✓

Answer

Correct option: A.

$\sin x + {c_1}x + {c_2}$

a
(a) We have, $\frac{{{d^2}y}}{{d{x^2}}} + \sin x = 0$or $\frac{{{d^2}y}}{{d{x^2}}} = - \sin x$

On integrating, $\frac{{dy}}{{dx}} = - ( - \cos x) + {c_1}$ = $\cos x + {c_1}$

Again integrate, we get $y = \sin x + {c_1}x + {c_2}$.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from 9. differential equations→9. differential equations — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

The value of ${\sin ^{ - 1}}\,\left( {\frac{{12}}{{13}}} \right) - {\sin ^{ - 1}}\,\left( {\frac{3}{5}} \right)$ is equal to

If a + b + c = 0, then a × b =

c × a
b × c
0
Both (a) and (b)

Let $A=\left[a_{i j}\right]_{2 \times 2}$ where $a_{i j} \neq 0$ for all $i, j$ and $A^2=I$. Let a be the sum of all diagonal elements of $A$ and $b =| A |$, then $3 a ^2+4 b ^2$ is equal to

If $f(x) = \left\{ \begin{gathered} \,[x]\, + \,[ - x],\,\,x \ne 2 \hfill \\ \,\,\,\,\,\,\,\,\,\lambda \,\,\,\,\,\,\,\,\,,\,\,x = \,2\,\,\,\, \hfill \\ \end{gathered} \right.,$ then $f$ is continuous at $x = 2,$ provided $\lambda$ is (where $[.]$ is $G.I.F.$ )

The minimum distance between a point on the curve $y=e^x$ and a point on the curve $y=\log _e x$ is

If P(3, 2, -4), Q(5, 4, -6) and R(9, 8, -10) are collinear, then R divided PQ in the ratio:

3 : 2 internally
3 : 2 externally
2 : 1 internally
2 : 1 externally

$\int_{}^{} {\frac{{{e^{m{{\tan }^{ - 1}}x}}}}{{1 + {x^2}}}dx} $ equals to

Let $f:(2, \infty) \rightarrow N$ be defined by $f(x)=$ the largest prime factor of $[x]$. Then, $\int \limits_2^8 f(x) d x$ is equal to

Let $A =\left[\begin{array}{ll} a & b \\ c & d \end{array}\right]$ and $B =\left[\begin{array}{l}\alpha \\ \beta\end{array}\right] \neq\left[\begin{array}{l}0 \\ 0\end{array}\right]$ such that
$AB = B$ and $a + d =2021,$ then the value of $ad - bc$ is equal to ...... .

Let $f(x)=\sin x+\left(x^3-3 x^2+4 x-2\right) \cos x$ for $x \in(0,1)$ Consider the following statements

$I.$ $f$ has a zero in $(0,1)$

$II.$ $f$ is monotone in $(0,1)$ Then,