If y=5 -3 , prove that d^2y dx^2 +y=0 - Vidyadip

Question

$\text{If y}=5\cos\text{x}-3\sin\text{x},\text{ prove that }\frac{\text{d}^2\text{y}}{\text{dx}^2}+\text{y}=0$

✓

Answer

Let $\text{y}=5\cos\text{x}-3\cos\text{x}$
$\therefore\ \frac{\text{dy}}{\text{dx}}=-5\sin\text{x}-3\cos\text{x}$
$\Rightarrow\ \frac{\text{d}^2\text{y}}{\text{dx}^2}=-5\cos\text{x}+3\sin\text{x}=-(5\cos\text{x}-3\sin\text{x})=-\text{y}$
$\Rightarrow\ \frac{\text{d}^2\text{y}}{\text{dx}^2}=-\text{y}\ \Rightarrow\ \frac{\text{d}^2\text{y}}{\text{dx}^2}+\text{y}=0$

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 "3 Marks Question" from CONTINUITY AND DIFFERENTIABILITY→CONTINUITY AND DIFFERENTIABILITY — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Find the second order derivatives of the following functions:
$\text{y}=\log(\log\text{x})$

Prove the following results
$\tan\Big(\sin^{-1}\frac{15}{13}+\cos^{-1}\frac{3}{5}\Big)=\frac{63}{16}$

Evaluate the following integrals:
$\int\cot^5\text{x}\text{ cosec}^4\text{x}\text{ dx}$

Show that $\text{f}(\text{x})=\tan^{-1}\text{x}-\text{x}$ is a decreasing function on R.

If $\text{y}=\log(\sin\text{x})$ Prove that $\frac{\text{d}^3\text{y}}{\text{dx}^3}=2\cos\text{x}\ \text{cosec}^3\text{x}$

If $e^{x+y} - x = 0$, prove that $\frac{\text{dy}}{\text{dx}}=\frac{1-\text{x}}{\text{x}}$

Verify Mean Value Theorem, if $f(x) = x^3 – 5x^2 – 3x$ in the interval $[a, b]$, where $a = 1$ and $b = 3$. Find all $\text{c}\in(1,\ 3)$ for which $f′(c) = 0$.

Using the properties of determinants:
$\begin{vmatrix}0&\text{xy}^2&\text{xz}^2\\\text{x}^2\text{y}&0&\text{yz}^2\\\text{x}^2\text{z}&\text{zy}^2&0\end{vmatrix}$

Evaluate the following integrals:
$\int\sqrt{\tan\text{x}}\sec^4\text{x}\text{ dx}$

Find the interval for which function $f(x)=2 \log (x-2)-x^2+4 x+1$ is increasing.