Q. 23.6( 67 Votes )
In each of the question, form a differential equation representing the given family of curves by eliminating arbitrary constants a and b.
y2 = a(b2 – x2)
Answer :
The given equation is y2 = a(b2 – x2)
Now, differentiating both sides w.r.t x, we get,
⇒ 2yy’ = -2ax
⇒ yy’ = -ax -------(1)
Now, again differentiating both sides, we get,
y’.y’ +yy’’ = -a
⇒ (y’)2 + yy” = -a --------(2)
Now, dividing equation (2) by (1), we get,
⇒ xyy” + x(y’)2 – yy” = 0
Therefore, the required differential equation is xyy” + x(y’)2 – yy” = 0.
Rate this question :
Interactive Quiz on DIfferential Calculus50 mins
Interactive Quiz on Differential Calculus | Check Yourself56 mins
Functional Equations - JEE with ease48 mins
Solve the following differential equation:
tan-1x + tan-1 y = c is the general solution of the differential equation:
Mathematics - ExemplarThe number of solutions of 
when y(1) = 2 is:
Find the particular solution of the differential equation
given that 
when 
Solve the following differential equation:
dy + (x + 1)(y + 1) dx = 0
RD Sharma - Volume 2Find the particular solution of the following differential equation:
when x = 1
