JEE PYQ: Differential Equation Question 15
Question 15 - 2021 (26 Feb Shift 1)
The difference between degree and order of differential equation that represents the family of curves given by $y^2 = a\left(x + \frac{\sqrt{a}}{2}\right)$, $a > 0$ is ______.
Show Answer
Answer: 2
Solution
$y^2 = ax + a^{3/2}/2$. Differentiating: $2yy’ = a$. So $a = 2yy’$. Substituting: $y^2 = 2yy’x + (2yy’)^{3/2}/2$. Squaring to remove the $3/2$ power: $(y-2xy’)^2 = 2y(y’)^3 \cdot y$. This is degree 3, order 1. Difference $= 3 - 1 = 2$.
BETA
