Find the solution of d y d x =2^ y-x - Vidyadip

Question

Find the solution of $\frac{d y}{d x}=2^{y-x}$

✓

Answer

Given that,$\frac{d y}{d x}=2^{y-x}$
$\Rightarrow \quad \frac{d y}{d x}=\frac{2^y}{2^x}$ $\left[\because a^{m-n}=\frac{a^m}{a^n}\right]$
$\Rightarrow \quad \frac{d y}{2^y}=\frac{d y}{2^x}$
On integrating both sides,we get
$\int 2^{-y} d y=\int 2^{-x} d x$
$\Rightarrow \quad \frac{-2^{-y}}{\log 2}=\frac{-2^{-x}}{\log 2}+C$
$\begin{array}{l}\Rightarrow-2^{-y}+2^{-x}=+C \log 2 \\ \Rightarrow \quad 2^{-x}-2^{-y}=-C \log 2\end{array}$
$\Rightarrow \quad 2^{-x}-2^{-y}=k \quad[$ where, $k=+C \log 2]$

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 Differential Equations and Modeling→Differential Equations and Modeling — all question types→Applied Maths STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

Prove that: $\int_0^a f(x) d x=\int_0^a f(a-x) d x$

Construct 5-yearly moving averages from the following data of the number of industrial failures in a country during 2003-2018:

Year	No. of failures
2003	23
2004	26
2005	28
2006	32
2007	20
2008	12
2009	12
2010	10
2011	9
2012	13
2013	11
2014	14
2015	12
2016	9
2017	3
2018	1

If $x=-9$ is a root of $\left|\begin{array}{lll}x & 3 & 7 \\ 2 & x & 2 \\ 7 & 6 & x\end{array}\right|=0$, then find the other two roots.

Mr. X took a loan of ₹2,000 for 6 months. Lender deducts ₹200 as interest while lending. Find the effective rate of interest charged by lender.

Define Producer Surplus.

600 gm of jaggery syrup has $40 \%$ jaggery in it. How much jaggery should be added to make it $50 \%$ in the syrup?

The incidence of occupational disease in an industry is such that the workers have a 20% chance of suffering from it. What is the probability that out of six workers 4 or more will catch the disease?

Eight coins are tossed together. The probability of getting exactly 3 heads.

Mr. X and Mr. Y have net worth of 1.93 crores INR and -0.22 crores INR. Represent the above information in the form of inequality.