The solution of the differential equation (1 + x^2 ) dy dx = x is - Vidyadip

MCQ

The solution of the differential equation $(1 + {x^2})\frac{{dy}}{{dx}} = x$ is

A
$y = {\tan ^{ - 1}}x + c$
B
$y = - {\tan ^{ - 1}}x + c$
✓
$y = \frac{1}{2}{\log _e}(1 + {x^2}) + c$
D
$y = - \frac{1}{2}{\log _e}(1 + {x^2}) + c$

✓

Answer

Correct option: C.

$y = \frac{1}{2}{\log _e}(1 + {x^2}) + c$

c
(c) $(1 + {x^2})\frac{{dy}}{{dx}} = x$==> $dy = \frac{x}{{1 + {x^2}}}dx$

==> $\int {dy} = \int {\frac{x}{{1 + {x^2}}}dx} + c$ ==> $y = \frac{1}{2}{\log _e}(1 + {x^2}) + c$.

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

Choose the correct answer:
Area lying between the curves y² = 4x and y = 2x is:

$\frac23$
$\frac13$
$\frac14$
$\frac34.$

The region formed by the inequalities $2 x+3 y-5 \leq 0,4 x-3 y+2 \leq 0$ and $x \geq 0 \ldots \ldots \ldots$

If $A$ is square matrix such that $A^{2}=A$, then $(1+A)^{3}-7 A$ is equal to

Given $f(x)=$ $\begin{cases}
\frac{ln(1+sgn[x]+{x}^2)}{1-cos{x}} & \text{ if } x\neq0 \\
& k\text{ if } x= 0
\end{cases}$ then

(where [.], {.} and $sgn\ x$ denotes greatest integer function, fractional part function and signum function respectively)

If $A = [1\,\,2\,{\rm{ }}3]$and $B = \left[ {\begin{array}{*{20}{c}}{ - 5}&4&0\\0&2&{ - 1}\\1&{ - 3}&2\end{array}} \right]$, then $AB = $

If $\left|\begin{array}{lll}\alpha & 3 & 4 \\ 1 & 2 & 1 \\ 1 & 4 & 1\end{array}\right|=0$, then the value of $\alpha$ is

Let $f :R \to R$ be a function defined as $f\left( x \right) = \left\{ \begin{array}{l}
5,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,if\,\,\,\,\,\,\,x \le 1\,\,\,\,\,\,\,\\
a + bx,\,\,\,\,if\,\,\,\,\,\,1 < x < 3\\
b + 5x,\,\,\,\,if\,\,\,\,\,\,3 \le x < 5\\
30,\,\,\,\,\,\,\,\,\,\,if\,\,\,\,\,\,\,x \ge 5
\end{array} \right.\,\,\,\,$ Then $f$ is

Let the function f : R - {-b} → R - {1} be defined by $\text{f(x)}=\frac{\text{x}+\text{a}}{\text{x}+\text{b}},\ \text{a}\neq\text{b}.$ Then,

f is one-one but not onto.
f is onto but not one-one.
f is both one-one and onto.
None of these.

$\int {\frac{{dx}}{{{x^2} + 4x + 13}}} $ is equal to

The function which is continuous for all real values of $x$ and differentiable at $x = 0$ is