Download App

Higher Order Derivatives — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSHigher Order Derivatives3 Marks
Question
If $\text{y}=\text{ae}^{2\text{x}}+\text{be}^{-\text{x}},$ show that $\frac{\text{d}^2\text{y}}{\text{dx}^2}-\frac{\text{dy}}{\text{dx}}-2\text{y}=0$
✓

Answer

Here,
$\text{y}=\text{ae}^{2\text{x}}+\text{be}^{-\text{x}}$
Differentiating w.r.t.x, we get
$\frac{\text{dy}}{\text{dx}}=2\text{a}\text{e}^{2\text{x}}$
Differentiating w.r.t.x, we get
$\Rightarrow\frac{\text{d}^2\text{y}}{\text{dx}^2}=4\text{a}\text{e}^{2\text{x}}$
$\Rightarrow\frac{\text{d}^2\text{y}}{\text{dx}^2}=2\text{a}\text{e}^{2\text{x}}$
$\Rightarrow\frac{\text{d}^2\text{y}}{\text{dx}^2}=\frac{\text{dy}}{\text{dx}}+2\text{y}$
$\Rightarrow\frac{\text{d}^2\text{y}}{\text{dx}^2}-\frac{\text{dy}}{\text{dx}}-2\text{y}=0$
Hence proved.

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 Higher Order Derivatives→Higher Order Derivatives — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

Find the angle between the vectors  $\hat{i}-2\hat{j}+3\hat{k}\ \text{and}\ 3\hat{i}-2\hat{j}+\hat{k}.$
→
Find the area of a triangle whose vertices are $A(1,1,1), B(1,2,3)$ and $C(2,3,3)$.
→
Evaluate the following integrals:$\int\frac{\text{e}^\text{x}}{(1+\text{e}^{\text{x}})(2+\text{e}^\text{x})}\text{dx}$
→
Evaluate the following integrals:
$\int(\text{a}\tan\text{x}+\text{b}\cot \text{x})^2\text{dx}$
→
Represent the following families of curves by forming the corresponding differential equation:
$\text{y}=\text{ax}^3$
→
Examine the consistency of the system of equation 5x - y + 4z = 5; 2x + 3y + 5z = 2; 5x - 2y + 6z = - 1
→
Find the approximate change in the value $V$ of a cube of side $x$ metres caused by increasing the side by $1\%.$
→
Evaluate the following definite integrals:
$\int_{0}^\limits{1}\frac{1}{\sqrt{1+\text{x}}-\sqrt{\text{x}}}\text{ dx}$
→
Evaluate the following integrals:
$\int^\limits9_0\text{f(x)}\text{dx},$ Where $\text{f(x)}=\begin{cases}\sin\text{x},&0\leq\text{x}\leq\frac{\pi}{2}\\1,&\frac{\pi}{2}\leq\text{x}\leq3\\\text{e}^{\text{x}-3},&3\leq\text{x}\leq9\end{cases}$
→
If in a binomial distribution n = 4 and P(X = 0) $=\frac{16}{81},$ find q.
→