Question

Solve: sin px cos y = Cos px sin y+p.
​

Answer 1

Answer:

The given differential equation is  sin y cos Px – cos y sin Px – P = 0 sin(y – Px) = P (y – Px) = sin–1(P) y = Px + sin–1(P) which is a Clairaut differential equation. Hence, the solution is y = cx + sin–1(c)Read more on Sarthaks.com - https://www.sarthaks.com/564011/solve-sin-y-cos-px-cos-y-sin-px-p-0

Answer 2

Answer:

Correct options are A) , C) and D)

The given equation can be written as px−y=sin

−1

p

Differentiating w.r.t x, both sides

(x−

1−p

2

1

)

dx

dp

=0⇒p=c or x=

1−p

2

1

Putting p=c in the equation we have cx−y=sin

−1

c

Also x=

1−p

2

1

⇒p=

x

x

2

−1

∴y=

x

2

−1

−sin

−1

x

x

2

−1

⇒y=0 is a solution