The solution of dy dx + y 3 = 1 is - Vidyadip

MCQ

The solution of $\frac{{dy}}{{dx}} + \frac{y}{3} = 1$ is

A
$y = 3 + c{e^{x/3}}$
✓
$y = 3 + c{e^{ - x/3}}$
C
$3y = c + {e^{x/3}}$
D
$3y = c + {e^{ - x/3}}$

✓

Answer

Correct option: B.

$y = 3 + c{e^{ - x/3}}$

b
(b) Given, $\frac{{dy}}{{dx}} + \frac{y}{3} = 1$; $I.F.$ = ${e^{\int {\frac{1}{3}\,d\,x} }} = {e^{x/3}}$

Hence, solution is $y\,.\,{e^{x/3}} = \int {1\,.\,{e^{x/3}}\,dx + c} $

$y\,.\,{e^{x/3}} = 3\,{e^{x/3}} + c$; $y = 3 + c{e^{ - x/3}}$.

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 9. differential equations→9. 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

Let $\mathrm{f}(\mathrm{x})$ be a polynomial of degree $5$ such that $\mathrm{x}=\pm 1$ are its critical points. $\mathop {\lim }\limits_{x \to 0} \left(2+\frac{f(x)}{x^{3}}\right)=4,$ then which one of the following is not true?

If $\theta$ is the angle between two vectors $\vec{\text{a}}$ and $\vec{\text{b}},$ then $\vec{\text{a}}.\vec{\text{b}}\geq0$ only when:

$0<\theta\frac{\pi}{2}$
$0\leq\theta\leq\frac{\pi}{2}$
$0<\theta<\pi$
$0\leq\theta\leq\pi$

For every point P(x, y, z) on the xy-plane,

x = 0
y = 0
z = 0
x = y = z = 0

The maximum volume (in $cu.m$) of the right circular cone having slant height $3\, m$ is

If $a = (1,\,\, - 1)$ and $b = ( - \,2,\,m)$ are two collinear vectors, then $m =$

Choose the correct option from given four options:
$\int\frac{\text{x}+\sin\text{x}}{1+\cos\text{x}}\text{dx}$ is equal to:

$\log|1+\cos\text{x}|+\text{C}$
$\log|\text{x}+\sin\text{x}|+\text{C}$
$\text{x}-\tan\frac{\text{x}}{2}+\text{C}$
$\text{x}\cdot\tan\frac{\text{x}}{2}+\text{C}$

If $a{x^2} + 2hxy + b{y^2} + 2gx + 2fy + c = 0$, then ${{dy} \over {dx}} = $

Let $A =\left[\begin{array}{ll} a & b \\ c & d \end{array}\right]$ and $B =\left[\begin{array}{l}\alpha \\ \beta\end{array}\right] \neq\left[\begin{array}{l}0 \\ 0\end{array}\right]$ such that
$AB = B$ and $a + d =2021,$ then the value of $ad - bc$ is equal to ...... .

If $\left(\sin ^{-1} x\right)^{2}-\left(\cos ^{-1} x\right)^{2}=a ; 0\,<\,x\,<\,1, a \neq 0$, then the value of $2 \mathrm{x}^{2}-1$ is :

If $\text{f(x)}=\begin{vmatrix}0&\text{x}-\text{a}&\text{x}-\text{b}\\\text{x}+\text{a}&0&\text{x}-\text{c}\\\text{x}+\text{b}&\text{x}+\text{c}&0\end{vmatrix},$ then:

f(a) = 0
f(b) = 0
f(0) = 0
f(1) = 0