The order of the differential equation whose general solution is … - Vidyadip

MCQ

The order of the differential equation whose general solution is given by $y = ({c_1} + {c_2})$ $\cos (x + {c_3}) - {c_4}{e^{x + {c_5}}},$ where ${c_1},\;{c_2},\;{c_3},\;{c_4},\;{c_5}$ are arbitrary constants, is

A
$5$
B
$4$
✓
$3$
D
$2$

✓

Answer

Correct option: C.

$3$

c
(c) $y = ({c_1} + {c_2})\cos (x + {c_3}) - {c_4}{e^{x + {c_5}}}$
${y_1} = - ({c_1} + {c_2})\sin (x + {c_3}) - {c_4}{e^{x + {c_5}}}$
${y_2} = - ({c_1} + {c_2})\cos (x + {c_3}) - {c_4}{e^{x + {C_5}}} = - y - 2{c_4}{e^{x + {c_5}}}$
==> ${y_3} = - {y_1} - 2{c_4}{e^{x + {c_5}}} = - {y_1} + {y_2} + y$
Hence the differential equation is ${y_3} - {y_2} + {y_1} - y = 0$, which is of order $3$.

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 STD 12 - 9. differential equations→STD 12 - 9. differential equations — all question types→Mathematics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

Area of a rectangle having vertices A, B, C and D with position vectors $-\hat{i}+\frac{1}{2}\hat{j}+4\hat{k},\ \hat{i}+\frac{1}{2}\hat{j}+4\hat{k},$ $\hat{i}-\frac{1}{2}\hat{j}+4\hat{k}\ \text{and} \ -\hat{i}-\frac{1}{2}\hat{j}+4\hat{k},$

Which of the following sets are convex?

A and B are two events such that P(A) = 0.25 and P(B) = 0.50. The probability pf both happening together is 0.14. The probability of both A and B hot happening is.

$\sin \left(\tan ^{-1} x\right)$, where $|x|<1$, is equal to

Consider the following statements in respect of the differential equation $\frac{\text{d}^2\text{y}}{\text{d}\text{x}^2}+\cos\Big(\frac{\text{dx}}{\text{dy}}\Big)=0:$
1. The degree of the differential equation is not defined.
2. The order of the differential equation is 2.
Which of the above statements is/are correct ?

Let $\mathrm{f}: \mathrm{R}-\left\{\frac{-1}{2}\right\} \rightarrow \mathrm{R}$ and $\mathrm{g}: \mathrm{R}-\left\{\frac{-5}{2}\right\} \rightarrow \mathrm{R}$ be defined as $f(x)=\frac{2 x+3}{2 x+1}$ and $g(x)=\frac{|x|+1}{2 x+5}$. Then the domain of the function $fog$ is:

A bag contains 5 red and 3 blue balls. If 3 balls are drawn at random without replacement the probability of getting exactly one red ball is

Let $f(\mathrm{x})=\mathrm{x}^5+2 \mathrm{e}^{\mathrm{x} / 4}$ for all $\mathrm{x} \in \mathrm{R}$. Consider a function $g(x)$ such that $(gof) (x)=x$ for all $x \in R$. Then the value of $8 g^{\prime}(2)$ is :

The area of smaller part between the circle ${x^2} + {y^2} = 4$ and the line $x = 1$ is

If $\text{f}(\text{x})=\text{e}^{\cos^{-1}\big\{\sin\big(\text{x}+\frac{\pi}{3}\big)\big\}}$ then $\text{f}\Big(\frac{8\pi}{9}\Big)=$