The differential equation representing the family of curves $y ^2= 2c (x+ \sqrt{c} ), $ where c is a positive parameter , is of
Answer & explanation
Correct answer: option 1
The correct answer is option (1) : Order 1 and degree 3
We have,
$y^2 = 2c(x+ \sqrt{c})$ ..................(i)
$⇒2y\, y _1= 2c$
$⇒y y_1= c $ .............(ii)
Eliminating c from (i) and (ii), we get
$y^2 = 2y\, y_1(x+ \sqrt{yy_1})$
$⇒y - 2xy_1= (\sqrt{u}y_1)^{3/2}⇒(y-2xy_1)^2=(yy_1)^3$
Clearly, it is a differential equation of order 1 and degree 3.