What will be the general solution of differential equation for 2^x – y dx + 2^y – x dy = 0?

Category: QuestionsWhat will be the general solution of differential equation for 2^x – y dx + 2^y – x dy = 0?
Editor">Editor Staff asked 11 months ago

What will be the general solution of differential equation for 2^x – y dx + 2^y – x dy = 0?
 
(a) 2^2x + 2^2y = c
 
(b) 2(2^2x + 2^2y) = c
 
(c) 3(2^2x + 2^2y) = c
 
(d) 4(2^2x + 2^2y) = c
 
This question was posed to me during a job interview.
 
My question is from Linear First Order Differential Equations in portion Differential Equations of Mathematics – Class 12
NCERT Solutions for Subject Clas 12 Math Select the correct answer from above options 
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1 Answers
Editor">Editor Staff answered 11 months ago

Right answer is (a) 2^2x + 2^2y = c
 
To explain I would say: We have, 2^x – y dx + 2^y – x dy = 0
 
Or, (2^x/2^y)dx + (2^y/2^x)dy = 0
 
Integrating both sides,
 
∫2^2xdx + ∫2^2ydy = k
 
Taking k = c/2log2 as, k, c and 2log2 are constant.
 
Or, 2^2x/2log2 + 2^2y/2log2 = c/2log2
 
Or, 2^2x + 2^2y = c