The differential equation of y=c x +c^2 is - Vidyadip

MCQ

The differential equation of $y=\frac{c}{x}+c^2$ is

A
$x^4\left(\frac{d y}{d x}\right)^2-x\frac {d y}{d x}=y$
B
$\frac{d^2 y}{d x^3}+x \frac{d y}{d x}+y=0$
C
$x^3\left(\frac{d y}{d x}\right)^2+x\frac{d y}{d x}=y$
D
$\frac{d^2 y}{d x^2}+\frac{d y}{d x}-y=0$

✓

Answer

$y=\frac{c}{x}+c^2 ....(1)$
Differentiating w.r.t.x,
$\frac{d y}{d x}=\frac{-c}{x^2}+0$
$c=-x^2 \frac{ dy }{ dx }$......(2)
Putting in equation (1)
$y=\frac{-x^2 \frac{d y}{d x}}{x}+\left(-x^2 \frac{d y}{d x}\right)^2$
$y=-x \frac{d y}{d x}+x^4\left(\frac{d y}{d x}\right)^2$
$x^4\left(\frac{d y}{d x}\right)^2-x \frac{d y}{d x}=y$

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 "MCQ" from Differential Equations→Differential Equations — all question types→Maths STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

The point on the curve $y = 6x - x^2$ at which the tangent to the curve is inclined at $\frac{\pi}{4}$ to the line $x + y = 0$ is:

If $\text{A}=\begin{bmatrix}1&2&\text{x}\\0&1&0\\0&0&1\end{bmatrix}$ and $\text{B}=\begin{bmatrix}1&-2&\text{y}\\0&1&0\\0&0&1\end{bmatrix}$ and $AB = I_3$, then $x + y$ equals:

Consider 5 independent Bernoulli's trials each with probability of success $p$. If the probability of at least one failure is greater than or equal to $\frac{31}{32}$, then $p$ lies in the interval

The nature of straight lines represented by the equation $4 x^2+12 x y+9 y^2=0$ is

If $A=\left[\begin{array}{ccc}1 & 3 & -2 \\ -3 & 0 & -5 \\ 2 & 5 & 0\end{array}\right]$ and $A(\operatorname{adj} A)=K I$, then the value of $K$ is (where $I$ is unit matrix of order 3 )

If $|\bar{a}|=3,|\bar{b}|=5,|\bar{c}|=4$ and $\bar{a}+\bar{b}+\bar{c}=\overline{0}$, then the value of $(\bar{a} \cdot \bar{b}+\bar{b} \cdot \bar{c})$ is equal to

Which of the following equations represents a pair of real and coincident straight lines?

$\bar{a}$ and $\bar{b}$ are unit vectors. If $\bar{a}+\bar{b}$ is a unit vector, then the angle between $\overline{ a }$ and $\overline{ b }$ is

Given that p is ‘false’ and q is 'true' then the statement which is 'false' is

Let $x_0$ be the point of local minima of $f(x)=\vec{a} \cdot(\vec{b} \times \vec{c})$ where $\vec{a}=x \hat{i}-2 \hat{j}+3 \hat{k}$, $\vec{b}=-2 \hat{i}+x \hat{j}-\hat{k}, \vec{c}=7 \hat{i}-2 \hat{j}+x \hat{k}$, then the value of $\vec{a} \cdot \vec{b}$ at $x=x_0$ is