Question

If x=sin t y=sin pt show that (1-x^2)d^2y/dx^2 - xdy/dx+p^2y=0

Answer it with explanation ..

Points:-15☺

Answer 1

x =sint

dx/dt = cost

again,
y = sinpt

dy/dx = pcospt

so, dy/dx =pcospt/cost
d²y/dx =p{-psinpt.cost +sint.cospt }/cos²t.dt/dx

because x = sint
so (1-x²) =cos²t

so , (1-x²)d²y/dx²=-p²sinpt +ptant.copt

(1 -x²)d²y/dx² = -p²(sinpt) +p(cospt/cost)sint

put , sinpt =y

cospt/cost =dy/dx
and sint = x

now,
(1 - x²)d²y/dx² = -p²y +xdy/dx

(1 -x²)dy/dx -xdy/dx +p²y = 0

hence proved

Answer 2

Answer:

Hope this answer may help u mate