MCQ
The order of the differential equation whose solution is $y=a \cos x+b \sin x+c e^{-x}$ is
  • 3
  • B
    2
  • C
    1
  • D
    none of these

Answer

Correct option: A.
3
(a): $y=a \cos x+b \sin x+c e^{-x}$
It is a third order differential equation, as it contains three arbitrary constants.

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

Similar questions

In solving the $LP$ problem :

"Minimize $z=6 x+10 y$ subject to $x \geq 6, y \geq 2,2 x+y \geq 10, x \geq 0, y \geq 0$." redundant constraints are $....$

Let $\text{A}=\{\text{x}\in\text{R}:\text{x}\geq1\}.$ The inverse of the function f : A → A given by $\text{f(x)}=2^{\text{x}(\text{x}-1)},$ is:
Let a curve $y=y(x)$ be given by the solution of the differential equation

$\cos \left(\frac{1}{2} \cos ^{-1}\left(e^{-x}\right)\right) d x=\sqrt{e^{2 x}-1} \,d y$

If it intersects $y$-axis at $y=-1$, and the intersection point of the curve with $x$-axis is $(\alpha, 0)$ the $\mathrm{e}^{\alpha}$ is equal to $.....$

The solution of the differention equation $\frac{\text{dy}}{\text{dx}}=\frac{\text{x}^{2}+\text{xy}+\text{y}^{2}}{\text{x}^{2}}$ is:
If matrix $A$ and $B$ has order respectively $m \times n$ and $n \times p$ then order of AB is :
Which of the following statements could be true if, $f'' (x) = x^{1/3}$.  

$I$ $II$ $III$ $IV$
$f'(x) = \frac{9}{{28}} x^{7/3} +9$ $f (x) = \frac{9}{{28}} x^{7/3} -2$  $f (x) = \frac{3}{{4}}\,x^{4/3} +6$ $f'(x) =\frac{3}{{4}}\,x^{4/3} -4$

 

If $x = – 4$ is a root of $\triangle=\begin{bmatrix}\text{x}&2&3\\1&\text{x}&1\\3&2&\text{x}\end{bmatrix}=0,$ then the other roots are:
If $p = i - 2j + 3k$ and $q = 3i + j + 2k,$ then a vector along r which is linear combination of $ p$ and  $ q$  and also perpendicular to  $ q$ is
Given $f(x) = \int\limits_{ - 2}^x {t.g'(t)\,dt} $  for $x \geq  -2$, where $g$ is an increasing function, then 
The system of equations : $x + y + z = 5, x + 2y + 3z = 9, x + 3y + \lambda z = \mu$ has a unique solution, if