If y is a function of x then  (d2y/dx2) + y.(dy/dx) = 0.  If x is a function of y , then what does the same differential equation become ?

2 years ago

Share

Answers : (1)

                                        
Solution:
Let us assume a solution of the original differential equation as:
y=e^{ax}
Hence the given differential equation becomes:
a^{2}e^{ax}+ae^{2ax}=0 \Rightarrow e^{ax}=-a \Rightarrow y=\frac{logy}{x} \Rightarrow y^{1/y}=e^{x}

Thanks & Regards


Sumit Majumdar,


askIITians Faculty


Ph.D,IIT Delhi

5 months ago

Post Your Answer

More Questions On Integral Calculus

Ask Experts

Have any Question? Ask Experts
Post Question
 
Answer ‘n’ Earn
Attractive Gift
Vouchers
To Win!!!
Click Here for details
evaluate the following integral ∫ 1 / x(3 + log x) dx
 
 
Ans: Hello student, Please find the answer to your question below
  img
Jitender Singh 2 months ago
evaluate ∫ (1 – cos 2x) / (1 + cos 2x) dx
 
 
Ans: Hello Student, Please find answer to your question
  img
Jitender Singh 3 months ago
evaluate the following integral ∫ sin(x – alpha) / sin(x + alpha) dx
 
 
Ans: Hello student, Please find the answer to your question below
  img
Jitender Singh 2 months ago
Given two points a = (-2,0) and b =(0,4 ) the coordinate of a point M lying on the line 2x-3y=9 so that permeter of triangle amb is least , is
 
 
GIVEN QUESTION CAN BE SOLVED USING A.M-G.M INEQUALITY FOR PERIMETER TO BE MINIMUM AM +BM SHOULD BE MINIMUM i.e AM=BM OR SIMPLY M LIES ON PERPENDICULAR BISECTOR OF AB AND LINE2x-3y=9 i.e...
 
siddharth gupta 4 months ago
if [sqrt(a) + sqrt(b)]/ [sqrt(a) – sqrt(b)] + [sqrt(a) – sqrt(b)]/ [sqrt(a) + sqrt(b)] = a – b, then prove that a – b = sqrt (2)
 
 
Hello student, Please find the answer to your question below Given Taking lcm we get On expanding we get (a-b) 2 =2(a+b) so you get (a-b)= I think there is some error in the question
  img
SHAIK AASIF AHAMED 2 months ago
if |sinx+ cosx|=|sinx|+|cosx| then x belongs to which quadrant
 
 
the answer should be 1 Quadrant or 3 quadrant. Coz It will be true only when both of them will be positive or both will be negative.
 
Aditya Wahi 4 months ago
View all Questions »