If y=500e^ 7x +600e^ -7x , show that d^2y dx^2 =49y - Vidyadip

Question

$\text{If y}=500\text{e}^{7\text{x}}+600\text{e}^{-7\text{x}},\text{ show that }\frac{\text{d}^2\text{y}}{\text{dx}^2}=49\text{y}$

✓

Answer

$\text{y}=500\text{e}^{7\text{x}}+600\text{e}^{-7\text{x}}\dots(1)$
$\frac{\text{dy}}{\text{dx}}=3500\text{e}^{7\text{x}}-4200\text{e}^{-7\text{x}}$
$\frac{\text{d}^2\text{y}}{\text{dx}^2}=24500\text{e}^{7\text{x}}+29400\text{e}^{-7\text{x}}$
$\Rightarrow\ \frac{\text{d}^2\text{y}}{\text{dx}^2}=49(500\text{e}^{7\text{x}}+600\text{e}^{-7\text{x}})$
$\Rightarrow\ \frac{\text{d}^2\text{y}}{\text{dx}^2}=49\text{y}\ \ [\because\text{of }1]$

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 CONTINUITY AND DIFFERENTIABILITY→CONTINUITY AND DIFFERENTIABILITY — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

Write the value of $\cos\big(\sin^{-1}\text{x}+\cos^{-1}\text{x}\big),|\text{x}|\leq1$

Determine which of the following binary operations are associative and which are commutative:
'*' on N defined by a * b = 1 for all $\text{a, b}\in\text{N}.$

Integrate the function $\frac{3 x^{2}}{x^{6}+1}$

Find the equation of the plane with intercept 3 on the y-axis and parallel to ZOX plane.

Which of the following distributions of a random variable X are the probability distributions?

X:	0	1	2	3	4
P(X):	0.1	0.5	0.2	0.1	0.1

If a line has direction ratios proportional to 2, -1, -2, then what are its direction consines?

Evaluate the following integrals:
$\int\limits^\frac{\pi}{2}_0\cos^2\text{x}\text{ dx}$

A is a skew-symmetric of order 3, write the value of |A|.

If A = {3, 5, 7} and B = {2, 4, 9} and R is a relation given by "is less than", write R as a set ordered pairs.

Evaluate the following integrals:$\int\text{xe}^{2\text{x}}\text{dx}$