Download App

DIFFERENTIAL EQUATIONS — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSDIFFERENTIAL EQUATIONS1 Mark
MCQ
Which of the following is a homogeneous differnetial equation?
  • A
    $(4x + 6y + 5)dy - (3y + 2x + 4)dx = 0$
  • B
    $xy dx - (x^3 + y^3)dy = 0$
  • C
    $(x^3 + 2y^2)dx + 2xy dy = 0$
  • ✓
    $y^2dx + (x^2 - xy - y^2) = 0$
✓

Answer

Correct option: D.
$y^2dx + (x^2 - xy - y^2) = 0$
A differential equation is said to be homogenous if all
the in the terms in the equation have equal degree and it can be written in
the from $\frac{\text{dy}}{\text{dx}}=\frac{\text{f}(\text{x,}\text{y})}{\text{g}(\text{x,}\text{y})}.$In $(a), (b)$ and $(c),$
the degree of all the terms is not equal.
But in the equation $y^2 dx + (x^2- xy - y^2)dy = 0,$
the degree of all the terms is $2.$
Thus, $(d)$ constant a homogeneous differential equation.

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→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

If $\vec{a}, \vec{b}, \vec{c}$ are unit vectors such that $\vec{a}+\vec{b}+\vec{c}=\overrightarrow{0}$, then the value of $\vec{a} \cdot \vec{b}+\vec{b} \cdot \vec{c}+\vec{c} \cdot \vec{a}$ is
→
The function $\text{f(x)}=|\cos\text{x}|$ is:
  1. Everywhere continuous and differentiable.
  2. Everywhere continuous but not differentiable at $(2\text{n}+1)\frac{\pi}{2},\text{n}\in\text{Z}$
  3. Neither continuous nor differentiable at $(2\text{n}+1)\frac{\pi}{2},\text{n}\in\text{Z}$
  4. None of these.
→
If the curve $ay + x^2 = 7$ and $x^3 = y,$ cut orthogonally at $(1, 1),$ then the value of $a$ is:
→
The equation of the line passing through the points $\text{a}_1\hat{\text{i}}+\text{a}_2\hat{\text{j}}+\text{a}_3\hat{\text{k}}$ and $\text{b}\hat{\text{i}}+\text{b}_2\hat{\text{j}}+\text{b}_3\hat{\text{k}}$ is:
  1. $\vec{\text{r}}=\big(\text{a}_1\hat{\text{i}}+\text{a}_2\hat{\text{j}}+\text{a}_3\hat{\text{k}}\big)+\lambda\big(\text{b}_1\hat{\text{i}}+\text{b}_2\hat{\text{j}}+\text{b}_3\hat{\text{k}}\big)$
  2. $\vec{\text{r}}=\big(\text{a}_1\hat{\text{i}}+\text{a}_2\hat{\text{j}}+\text{a}_3\hat{\text{k}}\big)-\text{t}\big(\text{b}_1\hat{\text{i}}+\text{b}_2\hat{\text{j}}+\text{b}_3\hat{\text{k}}\big)$
  3. $\vec{\text{r}}=\text{a}_1(1-\text{t})\hat{\text{i}}+\text{a}_2(1-\text{t})\hat{\text{j}}+\text{a}_3(1-\text{t})\hat{\text{k}}+\text{t}\big(\text{b}_1\hat{\text{i}}+\text{b}_2\hat{\text{j}}+\text{b}_3\hat{\text{k}}\big)$
  4. $\text{None of these}$
→
Five persone entered the lift cabin on the ground floor of an $8$ floor house. Suppose that each of them independently and with equal probability can leave the cabin at any flor beginning with the first, then the probability of all $5$ persons leaving at different floors is,
→
$2\cos^{-1}\text{x}=\sin^{-1}(2\text{x}\sqrt{1-\text{x}^2})$ is true for:
  1. all x
  2. x > 0
  3. $\text{x }\epsilon[-1,1]$
  4. $\frac{1}{\sqrt{2}}\leq\text{x}\leq1$
→
If the equations $a x+4 y+z=0, b x+3 y+z=0, c x+2 y+z=0$ have non $-$ trivial solution, then find the value of $a-2 b+c$.
→
If the binary operation $\odot$ is defined on the set $Q^+$ of all positive rational numbers by $\text{a}\odot\text{b}=\frac{\text{ab}}4$. Then, $3\odot\Big(\frac{1}5\odot\frac{1}2\Big)$ is equal to:
→
The area of a triangle with vertices A, B, C is given by
→
If $\cos^{-1}\frac{\text{x}}{2}+\cos^{-1}\frac{\text{y}}{2}=\theta,$ then $\Rightarrow9\text{x}^2-12\text{xy}\cos\theta+4\text{y}^2$ is equal to:
  1. $36$
  2. $-36\sin^2\theta$
  3. $36\sin^2\theta$
  4. $-36\cos^2\theta$
→