Question

Find the General and singular
Solution of (y-px)² + a²p=0​

Answer 1

Answer:

Given the differential equation,

y=px+p−p

2

.......(1)

Now, differentiating both sides with respect to x we get,

p=p+(x+1−2p)

dx

dp

[ Since

dx

dy

=p]

or, (x+1−2p)

dx

dp

=0

or, x+1=2p and

dx

dp

=0.

or, p=

2

x+1

gives particular solution and

dx

dp

=0 leads to general solution.

Now putting p=

2

x+1

in (1) we get,

y=

2

(x+1)

2

−

4

(x+1)

2

or, y=

4

(x+1)

2

or, (x+1)

2

=4y.