The solution of the differential equation dy dx = 1 + y^2 1 + x^2… - Vidyadip

MCQ

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

A
$1 + xy + c(y + x) = 0$
B
$x + y = c(1 - xy)$
✓
$y - x = c(1 + xy)$
D
$1 + xy = c(x + y)$

✓

Answer

Correct option: C.

$y - x = c(1 + xy)$

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

Now on integrating both sides, we get

${\tan ^{ - 1}}y = {\tan ^{ - 1}}x + {\tan ^{ - 1}}c$==> ${\tan ^{ - 1}}y = {\tan ^{ - 1}}\left( {\frac{{x + c}}{{1 - cx}}} \right)$

==> $y = \frac{{x + c}}{{1 - cx}}$ ==> $y - x = c(1 + xy)$.

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

The lateral edge of a regular hexagonal pyramid is $1 cm$. If the volume is maximum, then its height must be equal to

If $y=y(x)$ and it follows the relation $4x{e^{xy}} = y + 5{\sin ^2}x$ ,then $y'(0)$ is equal to

The vector $\left( {\hat i \times \vec a.\vec b} \right)\hat i + \left( {\hat j \times \vec a.\vec b} \right)\hat j + \left( {\hat k \times \vec a.\vec b} \right)\hat k$ is equal to

Let $x=x(y)$ be the solution of the differential equation $2 y \,e^{x / y^{2}} d x+\left(y^{2}-4 x e^{x / y^{2}}\right) d y=0$ such that $x(1)=0$. Then, $x(e)$ is equal to

The order and degree of the differential equation $x\frac{{{d^2}y}}{{d{x^2}}} + {\left( {\frac{{dy}}{{dx}}} \right)^2} + {y^2} = 0$ are respectively

Out of 30 consecutive integers, 2 are chosen at random. The probability that their sum is odd, is

The inverse matrix of $\left[ {\begin{array}{*{20}{c}}0&1&2\\1&2&3\\3&1&1\end{array}} \right],$ is

The projection of the vector $i+j+k$ along the vector $j$ is

Choose the correct answer from given four options in each of the Exercise : The area of a triangle with vertices $(-3, 0), (3, 0)$ and $(0, k)$ is $9$ sq. units. The value of $k$ will be:

If the volume of a spherical balloon is increasing at the rate of $ 900$ $cm^3$ $per\, sec$ , then the rate of change of radius of balloon at instant when radius is $ 15\,cm$ [ in $cm/sec$ ]