Differential EquationEasy
Question
The differential equation representing the family of curves y2 = 2c (x + √c), where c > 0, is a parameter, is of order and degree as follows:
Options
A.order 1, degree 2
B.order 1, degree 1
C.order 1, degree 3
D.order 2, degree 2
Solution
y2 = 2c(x + √c) ....(i)
2yy′ = 2c.1 or yy′ = c ....(ii)
y2 = 2yy′
[on putting value of c from (ii) in (i)]
On simplifying, we get
(y - 2xy′)2 = 4yy′3 ....(iii)
Hence equation (iii) is of order 1 and degree 3.
2yy′ = 2c.1 or yy′ = c ....(ii)
y2 = 2yy′
[on putting value of c from (ii) in (i)]On simplifying, we get
(y - 2xy′)2 = 4yy′3 ....(iii)
Hence equation (iii) is of order 1 and degree 3.
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