Download App

DIFFERENTIAL EQUATIONS — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsDIFFERENTIAL EQUATIONS4 Marks
Question
$\text{If}\ \text{y}=\sin(\sin\text{x}),\ \text{prove that}\frac{\text{d}^2\text{y}}{\text{dx}^2}+\tan\text{x}\frac{\text{dy}}{\text{dx}}+\text{y}\cos^2\text{x}=0.$
✓

Answer

$\text{y}=\sin(\sin\text{x})$
$\frac{\text{dy}}{\text{dx}}=\cos(\sin\text{x})\cos\text{x}$
$\frac{\text{d}^2\text{y}}{\text{dx}^2}=\cos(\sin\text{x})(-\sin\text{x})+\cos^2\text{x}[-\sin(\sin\text{x})]$
$\frac{\text{d}^2\text{y}}{\text{dx}^2}=-\sin\text{x}\cos(\sin\text{x})-\cos^2\text{x}\sin(\sin\text{x})$
$\text{L.H.S}=\frac{\text{d}^2\text{y}}{\text{dx}^2}+\tan\text{x}\frac{\text{dy}}{\text{dx}}+\text{y}\cos^2\text{x}$
$=-\sin\text{x}\cos(\sin\text{x})-\cos^2\text{x}\sin(\sin\text{x})\\+\tan\text{x}\cos\text{x}\cos(\sin\text{x})+\cos^2\text{x}\sin\text{x}(\sin\text{x})$
$=-\sin\text{x}\cos(\sin\text{x})+\frac{\sin\text{x}}{\cos\text{x}}\cos\text{x}\cos(\sin\text{x})$
$=-\sin\text{x}\cos(\sin\text{x})+\sin\text{x}\cos(\sin\text{x})$
$=0=\text{R.H.S.}$

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 "4 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

Solve the following differential equation
$\frac{\text{dy}}{\text{dx}}=(\text{e}^\text{x}+1)\text{y}$
→
Verify mean value theorem for the function:
$\text{f(x)}=\sqrt{25-\text{x}^2}\text{ in }[1,5].$
→
$\int\frac{2-3\text{x}}{\sqrt{1+3\text{x}}}\text{dx}$
→
In a class, 5% of the boys and 10% of the girls have an IQ of more than 150. In this class, 60% of the students are boys. If a student is selected at random and found to have an IQ of more than 150, find the probability that the student is a boy.
→
Integrate the rational function $\frac{3 x+5}{x^{3}-x^{2}-x+1}$
→
The mean and variance of a binomial variate with parameters n and p are 16 and 8, respectively. Find P(X = 0), P (X = 1) and P (X ≥ 2).
→
Evaluate the following integrals:
$\int\sqrt{1+\text{x}-2\text{x}^2}\text{dx}$
→
Find the equation of the plane mid-parallel to the planes 2x - 2y + z + 3 = 0 and 2x - 2y + z + 9 = 0
→
Five bad oranges are accidently mixed with 20 good ones. If four oranges are drawn one by one successfully with replacement, then find the probability distribution of number of bad oranges drawn. Hence find the mean and variance of the distribution.
→
$\begin{vmatrix}1+\text{a}&1&1\\1&1+\text{a}&\text{a}\\1&1&1+\text{a}\end{vmatrix}=\text{a}^3+3\text{a}^2$
→