Question Number 115000 by mnjuly1970 last updated on 22/Sep/20

....nice math... if y =(cos(2x))^(−(1/2)) then prove :: y+y^(′′) = 3y^5 ...m.n.july.1970...

Answered by Dwaipayan Shikari last updated on 22/Sep/20

y=(1/( (√(cos2x)))) y′=cos^(−(3/2)) 2x.sin2x y′′=3cos^(−(5/2)) 2x.sin^2 2x+2cos^(−(1/2)) 2x y+y′′=3(cos^(−(5/2)) 2x(1−cos^2 2x)+cos^(−(1/2)) 2x) y+y′′=3cos^(−(5/2)) 2x−3cos^(−(1/2)) 2x+3cos^(−(1/2)) 2x y+y′′=3y^5

Commented bymnjuly1970 last updated on 22/Sep/20

very nice very nice ...thank you sir...

Commented byCanovas last updated on 29/Sep/20

Correct

Answered by $@y@m last updated on 23/Sep/20

y=(1/( (√(cos 2x)))) y^2 =sec2 x ...(1) 2yy′=2sec2xtan 2x yy′=sec2xtan 2x yy′=y^2 tan2 x y′=ytan 2x ...(2) y′′=2ysec ^2 2x+tan2 x.y′ y′′=2y.y^4 +tan 2x.ytan 2x {using(1) &(2) y′′=2y^5 +ytan ^2 2x y′′=2y^5 +y(sec ^2 2x−1) y′′=2y^5 +y(y^4 −1) y+y′′=3y^5

Commented bymnjuly1970 last updated on 23/Sep/20

very nice awesom solution