The order of the differential equation whose solution is y=a x+b … - Vidyadip

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

Explore more

More "M.C.Q (1 Marks)" from Differential Equations→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

$\int\limits^\frac{\pi}{3}_\frac{\pi}{6}\frac{1}{\sin2\text{x}}\text{ dx}$ is equal to:

$\log_\text{e}{3}$
$\log_\text{e}\sqrt{3}$
$\frac{1}{2}\log(-1)$
$\log(-1)$

If $A = \left[ {\begin{array}{*{20}{c}}0&1\\0&0\end{array}} \right]$and $AB = O$, then $B =$

A tangent having slope of $-\frac{4}{3}$ to the ellipse $\frac{\text{x}^2}{18}+\frac{\text{y}^2}{32}=1$ ntersects the major and minor axes at points A and B respectively. If C is the center of the ellipse, then area of the triangle ABC is:

12 sq. units
24 sq. units
36 sq. units
48 sq. units

Construct a $3 \times 4$ matrix, whose elements are given by $a_{i j}=\frac{1}{2}|-3 i+j|$.

If $f(x) = \frac{{{e^{2x}} - {{(1 + 4x)}^{1/2}}}}{{\ln (1 - {x^2})}}$ for $x \ne 0,$ then $f$ has

Let $S$ be the set of all $\lambda \in \mathrm{R}$ for which the system of linear equations

$2 x-y+2 z=2$

$x-2 y+\lambda z=-4$

$x+\lambda y+z=4$

has no solution. Then the set $S$

Let $f:[-1,1] \rightarrow R$ be defined as $f(x)=a x^{2}+b x+c$ for all $x \in[-1,1],$ where $a , b , c \in R$ such that $f (-1)=2, f ^{\prime}(-1)=1$ and for $x \in(-1,1)$ the maximum value of $f ^{\prime \prime}( x )$ is $\frac{1}{2} .$ If $f ( x ) \leq \alpha$ , $x \in[-1,1],$ then the least value of $\alpha$ is equal to ...... .

Let $A=\left(\begin{array}{rrr}1 & -1 & 0 \\ 0 & 1 & -1 \\ 0 & 0 & 1\end{array}\right)$ and $B=7 A^{20}-20 A^{7}+2 I$, where $I$ is an identity matrix of order $3 \times 3$ If $B=\left[b_{i j}\right]$, then $b_{13}$ is equal to $....$

If $3{\sin ^{ - 1}}\frac{{2x}}{{1 - {x^2}}} - 4{\cos ^{ - 1}}\frac{{1 - {x^2}}}{{1 + {x^2}}} + 2{\tan ^{ - 1}}\frac{{2x}}{{1 - {x^2}}} = \frac{\pi }{3}$ then $x$ =

The area common to the parabola y = 2x² and y = x²+ 4 is:

$\frac{2}{3}\text{ sq. units}$
$\frac{3}{2}\text{ sq. units}$
$\frac{32}{3}\text{ sq. units}$
$\frac{3}{32}\text{ sq. units}$