Saturday

December 20, 2014

December 20, 2014

Posted by **shoosh** on Sunday, March 3, 2013 at 4:53pm.

(1-x^2)(d^2y/dx^2)-x(dy/dx)+n^2(dy/dx)=0

- math (differential equation) -
**Steve**, Sunday, March 3, 2013 at 5:16pmseems pretty straightforward:

y = cos(n arccos(x))

y' = n sin(n arccos(x)) / √(1-x^2)

y'' = nx sin(n arccos(x))/(1-x^2)^(3/2) - n^2 cos(n arccos(x))/(1-x^2)

(1-x^2) y'' = nx sin(n arccos(x))/√(1-x^2) - n^2 cos(n arccos(x))

(1-x^2) y'' - xy' = n^2 cos(n arccos(x))

(1-x^2) y'' - xy' - n^2 y' doesn't make it go to zero.

That last step doesn't seem right. Is there a typo? Just the way it's shown doesn't seem right; two separate terms with y'

**Answer this Question**

**Related Questions**

calculus-differential equation - Consider the differential equation: (du/dt)=-u^...

calculus - verify that y=c/x^2 is a general solution of the differential ...

CACULUS - dy/dx = (y-1)^2 cosπx There's a horizontal line with equation y=c...

math - The displacement s (in metres) of a body in a damped mechanical system, ...

Math - a weight of mass m is attached to a spring and oscillates with simple ...

Calculus-HELP!!!! - Show that the function y=c_1 e^x cos(x)+ c_2 e^x sin(x) ...

Differential Equations - Consider the differential equation: dy/dt=y/t^2 a) Show...

Differential Equations - Consider the differential equation: dy/dt=y/t^2 a) Show...

Calculus - Solve the differential equation dy/dx = -xe^y and determine the ...

Differential Equations - Consider the differential equation: dy/dt=y/t^2 a) Show...