MY CART (5)

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price:

There are no items in this cart.
Continue Shopping
                   

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 ?

3 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

9 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
What is the value of ∫ e -x (1-tanx)secx dx .
 
 
Hi, Just differentiate your answer with respect to x, if you are getting the original function (as in the question), then your answer is correct, otherwise wrong....
  img
Shobhit Varshney 5 months ago
 
Hi, Please use the integration formula by parts and take e-x to be first function and the remaining to be second...
  img
Shobhit Varshney 5 months ago
 
I just want the answer to see whether my answer is correct or not.
 
Shibashis Mallik 5 months ago
pi/2 ∫ 0 dx/1 + tan x
 
 
answer will be pi/4 ..see we have to use the property of definite integral f(a-x) = f(x). also change tanx to sinx / cosx now we have pi/2 ∫ 0 dx/1 + tan x = pi/2 ∫ 0 dx/ (1 + (sinx/cosx) )...
 
abhidon3 4 months ago
 
sorrythelast line was wrongly typed .. it was lower limit = 0 and upper limit = pi/2 of [1]* 1/2
 
abhidon3 4 months ago
5 ∫ 3 (2 – x) dx
 
 
integration of 2-x from 3 to 5 is equal to (2x-((x^2)/2)) from 3 to 5 =(2*5-((5^2)/2))-(2*3-((3^2)/2)) =(10-(25/2))-(6-(9/2)) =(-5/2)-(3/2) =-8/2 =-4
 
Miryala Gopalakrishna 5 months ago
 
Ans:- 5 ∫ 3 (2-x)dx =[2x-(x 2 /2)] 3 5 =[2(5-3)]-[(25/2)-(9/2)] =[2(2)]-[(25-9)/2] =4-8 =-4
 
Anusha 5 months ago
Sir pls solve this trigonometric eqn.
 
 
Dear student, We can rearange the given equation as: This equation wouldnt have any solution as: Since the function doesnt have a solution at the extremes and at the centre, we can assume...
  img
Sumit Majumdar 7 months ago
 
we can write given equation sinx = -cosec 2 x/2 but we know that minimum value of cosec 2 ø is 1 & maximum value of sinøis 1 simultaneously this is not possible sinx=-1...
  img
Sunil Raikwar 7 months ago
If each of the points (x1,4) , (-2,y1) lies on the line joining the points (2,-1),(5,-3) then the point P(x1,y1) lies on the lines ? Give the equation of that line.
 
 
equation of line joining (2,-1),(5,-3) is: 2x + 3y -1 = 0 Now (x1,4) , (-2,y1) lie on 2x + 3y -1 = 0. So it will satisfy. 2x 1 + 3*4 -1 = 0 and 2*-2 + 3y 1 -1 = 0 x 1 =-11/2 and y 1 = 5/3...
  img
Nishant Vora 5 months ago
 
Sir,Actually they are asking on which line x1,y1 lies :) ?
 
Aditya Pati 5 months ago
If XcosA +YsinA = p where p = – sin^2A/cos^2A be a straight line ,prove that the prependiculars on thisstraight line from the points ( m^2 , 2m ) , (Mm , M+m ) , ( M^2 ,2M ) form a geometric...
 
 
Length of perpendicular from a point (x1, y1) on a line ax+by+c=0 is the absolute value of : Use it to obtain the 3 perpendiculars and show that a1 2 = a 0 . a 2
  img
Ravi 4 months ago
View all Questions »