The solution of differential equation x dy dx + y = y^2 is - Vidyadip

MCQ

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

✓
$y = 1 + cxy$
B
$y = \log \{ cxy\} $
C
$y + 1 = cxy$
D
$y = c + xy$

✓

Answer

Correct option: A.

$y = 1 + cxy$

a
(a) $x\frac{{dy}}{{dx}} + y = {y^2}$ ==> $x\frac{{dy}}{{dx}} = {y^2} - y$

==> $\frac{{dy}}{{{y^2} - y}} = \frac{{dx}}{x}$ ==> $\left[ {\frac{1}{{y - 1}} - \frac{1}{y}} \right]dy = \frac{{dx}}{x}$

On integrating, we get $\log (y - 1) - \log y = \log x + \log c$

==> $\frac{{y - 1}}{y} = xc$ ==> $y = 1 + cxy$.

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

In a regular triangular prism the distance from the centre of one base to one of the vertices of the other base is $l.$ The altitude of the prism for which the volume is greatest

The corner points of the feasible region determined by the system of linear inequalities are (0, 0), (4, 0), (2, 4) and (0, 5). If the maximum value of z = ax + by, where a, b > 0 occurs at both (2, 4) and (4, 0), then:

The function $f: R \rightarrow R$ defined as $f(x)=x^3$ is

Let $\vec a\, = \,\hat i\, + \,2\hat j\, + 4\hat k\,,\,\vec b\, = \,\hat i\, + \,\lambda \hat j\, + 4\hat k$ and $\vec c\, = \,2\hat i\, + \,4\hat j\, + ({\lambda ^2} - 1)\hat k$ be coplanar vectors. Then the non -zero vector $\vec a\times \vec c$ is

If the adjoint of a $3 \times 3$ matrix $P$ is $\left[\begin{array}{lll}1 & 4 & 4 \\ 2 & 1 & 7 \\ 1 & 1 & 3\end{array}\right]$ then the possible value$(s)$ of the determinant of $P$ is (are)

$(A)$ $-2$ $(B)$ $-1$ $(C)$ $1$ $(D)$ $2$

The function $f : A \rightarrow B$ defined by $f(x) = -x^2 + 6x- 8$ is a bijection if,

The order of the differential whose general solution is given by ${\text{y}}=\text{C}_1\cos(2\text{x}+\text{C}_{2})+(\text{C}_{3}+\text{C}_{4})\text{a}^{\text{x}+\text{C}_{5}}+\text{C}_{6}\sin(\text{x}-\text{C}_{7}).$

If function $y = f(x)$ satisfy the differential equation $(x^3 + 1)dy = x(1 -3xy)dx$ and $f(0) = 0$ , then $\mathop {\lim }\limits_{x \to 0} \frac{{{x^2}}}{{f(x)}}$ is equal to

The value of $\int_{\, - 2}^{\,2} {\left[ {p\ln \left( {\frac{{1 + x}}{{1 - x}}} \right) + q\ln {{\left( {\frac{{1 - x}}{{1 + x}}} \right)}^{ - 2}} + r} \right]\,dx} $ depends on

$\int_1^e {\frac{1}{x}\,dx} $ is equals to