Download App

DIFFERENTIAL EQUATIONS — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSDIFFERENTIAL EQUATIONS2 Marks
Question
Solve the following differential equations:
$\frac{\text{dy}}{\text{dx}}=(\cos^2\text{x}-\sin^2\text{x})\cos^2\text{y}$
✓

Answer

$\frac{\text{dy}}{\text{dx}}=(\cos^2\text{x}-\sin^2\text{x})\cos^2\text{y}$
$\frac{\text{dy}}{\cos^2\text{y}}=(\cos^2\text{x}-\sin^2\text{x})\text{dx}$
$\int\sec^2\text{y dy}=\int\cos2\text{x dx}$
$\tan\text{y}=\frac{\sin2\text{x}}{2}+\text{C}$

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 "2 Marks Questions" from DIFFERENTIAL EQUATIONS→DIFFERENTIAL EQUATIONS — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

For each of the exercises given below, verify that the given function (implicit or explicit) is a solution of the corresponding differential equation.
$\text{y}=\text{a e}^{\text{x}}+\text{b e}^{-\text{x}}+\text{x}^2$ : $\text{x}\frac{\text{d}^2\text{y}}{\text{dx}^2}+2\frac{\text{dy}}{\text{dx}}-\text{xy}+\text{x}^2-2=0$
→
Define identity element for a binary operation defined on a set.
→
Find the values of a for which the functionf $( x)= \sin x - ax + 4$ is increasing function on $R$.
→
Find x, y satisfying the matrix equation.
$\begin{bmatrix}\text{x}-\text{y}&2&-2\\4&\text{x}&6\end{bmatrix}+\begin{bmatrix}3&-2&2\\1&0&-1\end{bmatrix}=\begin{bmatrix}6&0&0\\5&2\text{x}+\text{y}&5\end{bmatrix}$
→
Evaluate: $\begin{vmatrix}\cos15^\circ&\sin15^\circ\\\sin75^\circ&\cos75^\circ\end{vmatrix}$
→
If $A$ and $B$ are symmetric matrices, then write the condition for which $AB$ is also symmetric.
→
Evaluate $\int\frac{\text{x}^2}{1+\text{x}^3}\text{ dx}$
→
Evaluate the following integral:
$\int\frac{\text{x}^2-1}{\text{x}^2+4}\text{ dx}$
→
Find the unit vector in the direction of $3\hat{\text{i}}+4\hat{\text{j}}-12\hat{\text{k}}$.
→
Find a vector $\vec{\text{a}}$ of magnitude $5\sqrt2$, making an angle of $\frac{\pi}4$ with x-axis, $\frac{\pi}2$ with y-axis and an acute angle $\theta$ with z-axis.
→