Download App

Higher Order Derivatives — Maths STD 12 Science — Question

Maharashtra 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 "Solve the Following Question.(3 Marks)" from Higher Order Derivatives→Higher Order Derivatives — all question types→Maths STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

Show that $\text{f}(\text{x})=\text{x}-\sin\text{x}$ is increasing for all $\text{x}\in\text{R}.$
→
Evaluate :

$\int_3^5 \frac{1}{\sqrt{2 x+3} \sqrt{2 x-3}} \cdot d x$

→
Find the probability distribution of Y in two throws of two dice, where Y represents the number of times a total of 9 appears.
→
Differential equation $\frac{\text{dy}}{\text{dx}}+\text{y}=0,\text{y}(0)=3$Function $\text{y}=\text{e}^\text{-x}+2$
→
Differentiate the following functions with respect to x:
$\log_7(2\text{x}-3)$
→
If $f ^{\prime}( x )=x-\frac{3}{x^3}, f (1)=\frac{11}{2}$ find $f ( x )$
→
The direction ratios of $\overline{A B}$ are $-2,2$, 1. If $A=(4,1,5)$ and $I(A B)=6$ units, find $B$.
→
For what value of k the following distribution is a probability distributioin?
$X = x_i$ $0$ $1$ $2$ $3$
$P(X = x_i)$ $2k^4$ $3k^2 - 5k^3$ $2k - 3k^2$ $3k - 1$
→
The foot of the perpendicular drawn from the origin to a plane is M(1, 0, 0). Find the vector equation of the plane.
→
Determine that value of the constant 'k' so that function $\text{f(x)}=\begin{cases}\frac{\text{kx}}{|\text{x}|},&\text{if }\text{ x}<0\\3,&\text{if }\text{ x}\geq0\end{cases}$ is continuous at x = 0.
→