Trig! :P

[Lovely918]

Okay so I have work done on this problem but I want to know if I did it right:

So the question is : solve y"+y= sec(x)tan(x)

This is what I got:
r^2+1=0
r=+ or - i
c1cos x +c2 sin x

sin(v'1 cos x +v'2 cos^2 x=0
cos(-v'1 sin x +v'2 cos= sec x tan x)

v'2 sin^2 x + v'2 cos^2 x = cos/cos tan x
integral v'2=integral tan x
v2= ln sin x

v'1 cos^2 x +v'1 sin^2 x = (-sin/cos) tan x
-cot x tan x
integral v'1= integral -1
v1=-x
-x cos x +ln (absolute value of (sin x)) sin x
y= c1 cos x+c2 sin x- x cos x +ln (absolute value of (sin x) sin x

 

[Deleted member 4993]

Okay so I have work done on this problem but I want to know if I did it right:

So the question is : solve y"+y= sec(x)tan(x)

This is what I got:
r^2+1=0
r=+ or - i
c1cos x +c2 sin x

sin(v'1 cos x +v'2 cos^2 x=0
cos(-v'1 sin x +v'2 cos= sec x tan x)

v'2 sin^2 x + v'2 cos^2 x = cos/cos tan x
integral v'2=integral tan x
v2= ln sin x

v'1 cos^2 x +v'1 sin^2 x = (-sin/cos) tan x
-cot x tan x
integral v'1= integral -1
v1=-x
-x cos x +ln (absolute value of (sin x)) sin x
y= c1 cos x+c2 sin x- x cos x +ln (absolute value of (sin x) sin x

Differentiate your answer and plug those back into your original DE.

And you'll know.....