Download App

DIFFERENTIAL EQUATIONS — Maths STD 12 Science — Question

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

Similar questions

Evaluate the following integrals:
$\int\limits^\text{x}_{0}\text{e}^{-\text{x}}\text{ dx}$
→
Discuss the continuity of sine function.
→
Evaluate the following integral:
$\int\frac{1}{\sqrt{\text{a}^2-\text{b}^2\text{x}^2}}\text{ dx}$
→
If $x\left[\begin{array}{l}2 \\ 3\end{array}\right]+y\left[\begin{array}{c}-1 \\ 1\end{array}\right]=\left[\begin{array}{c}10 \\ 5\end{array}\right],$ find the values of $\mathrm{x}$ and $\mathrm{y}$.
→
Differentiate w.r.t. x the function in Exercise:
$\sin^3\text{x}+\cos^6\text{x}$
→
An insurance company insured $2000$ scooter drivers, $4000$ car drivers and $6000$ truck drivers. The probability of an accidents are $0.01, 0.03$ and $0.15$ respectively. One of the insured persons meet with an accident. What is the probability that he is a scooter driver?
→
Evaluate:
$\int\frac{\cos2\text{x}+2\sin^2\text{x}}{\sin^2\text{x}}\text{dx}$
→
Evaluate:
$\sin\Big(\tan^{-1}\text{x}+\tan^{-1}\frac{1}{\text{x}}\Big)\text{ for }\text{x}<0$
→
If either $\vec{a}=\vec {0}$ or $\vec{b}=\vec{0}$, then $\vec{a} \times \vec{b}=\vec 0$. Is the converse true? Justify your answer with an example.
→
Find the intervals in which the function $f$ given by $f(x)=2 x^3-3 x^2-36 x+7$ is decreasing.
→