Question

if y=cospt, x = cost, t belongs to (0,π/2) then (1-x²)y2 = ?
(a) xy1 - p²
(b) xy1 + p²y
(c)-xy1 - p²y
(d)-xy1 + p²y​

Answer 1

Answer:

Given x=sin t, y=cos pt

dx

dt

=cost

dy

dt

=-ψnpt

∴

dy

dx

=-

ψnpt

cost

⇒y1=

-p

√

1-y2

√

1-x2

⇒y1

√

1-x2

=-p

√

1-y2

⇒y

2

1

(1-x2)=p2(1-y2)

⇒2y1y2(1-x2)-2xy

2

1

=-2yy1p2 [differentiating]

⇒(1-x2)y2-xy1+p2y=0