The solution of the equation d y d x = ^2 y is :

MCQ

The solution of the equation $\frac{d y}{d x}=\cos ^2 y$ is :

A
$x+\tan y=c$
✓
$\tan y=x+c$
C
$\sin y+x=c$
D
$\sin y-x=c$

✓

Answer

Correct option: B.

$\tan y=x+c$

(B)
$
\begin{aligned}
\frac{d y}{d x} & =\cos ^2 y \\
\Rightarrow \quad \frac{1}{\cos ^2 y} d y & =d x \Rightarrow \sec ^2 y d y=d x
\end{aligned}
$
Hence
$
\begin{aligned}
\int \sec ^2 y d y & =\int d x \\
\tan y & =x+c
\end{aligned}
$
Therefore the correct choice is (B).

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

Similar questions

If $A=\left[\begin{array}{ccc}3 & -1 & 2 \\ 2 & 1 & 3 \\ 1 & -3 & K\end{array}\right]$ is non-invertible matrix, then value of K :

→

Let $\hat{u}=u_1 \hat{i}+u_2 \hat{j}+u_3 \hat{k}$ be a unit vector in $\mathbb{R}^3$ and $\hat{v}=\frac{1}{\sqrt{6}}(\hat{i}+\hat{j}+2 \hat{k})$. Given that there exists is(are) correct?

($A$) There is exactly one choice for such $\vec{v}$

($B$) There are infinitely many choices for such $\vec{v}$

($C$) If $\hat{u}$ lies in the $x y$-plane then $\left|u_1\right|=\left|u_2\right|$

($D$) If $\hat{u}$ lies in the $x z$-plane then $2\left|u_1\right|=\left|u_3\right|$

→

A spherical iron ball $10\, cm$ in radius is coated with a layer of ice of uniform thickness that melts at a rate of $50 cm^3/min$. When the thickness of ice is $ 5 cm$, then the rate at which the thickness of ice decreases, is

→

Consider the functions $f, g: R \rightarrow R$ defined by

$f(x)=x^2+\frac{5}{12}$ and $g(x)=\left\{\begin{array}{cc}2\left(1-\frac{4|x|}{3}\right), & |x| \leq \frac{3}{4} \\ 0, & |x|>\frac{3}{4}\end{array}\right.$

If $\alpha$ is the area of the region

$\left\{( x , y ) \in R \times R :| x | \leq \frac{3}{4}, 0 \leq y \leq \min \{f( x ), g( x )\}\right\},$

then the value of $9 \alpha$ is. . . . . .

→

Let $\overrightarrow{\mathrm{a}}=2 \hat{\mathrm{i}}+\hat{\mathrm{j}}-\hat{\mathrm{k}}, \overrightarrow{\mathrm{b}}=((\overrightarrow{\mathrm{a}} \times(\hat{\mathrm{i}}+\hat{\mathrm{j}})) \times \hat{\mathrm{i}}) \times \hat{\mathrm{i}}$.

Then the square of the projection of $\vec{a}$ on $\vec{b}$ is :

→

Mark the correct alternative in the following question : The probability of guessing correctly at least $8$ out of $10$ answers of a true false type examination is :

→

If $\text{y}=\tan^{-1}\Big(\frac{\sin\text{x}+\cos\text{x}}{\cos\text{x}-\sin\text{x}}\Big),$ then $\frac{\text{dy}}{\text{dx}}$ is equals to:

→

If a * b denote the bigger among a and b and if ab = (a * b) + 3, then 4.7 =