Latest Gate Aptitude Question SOLUTION: solve the differential equation........ (dy/dx)= (tan(2x+y+3))^2

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(#M40032506) GATE Numerical Ability question it's a D.Eqn, plzzzzz any one help me Keep an EYE

solve the differential equation........

(dy/dx)=
(tan(2x+y+3))^2

Asked In Gate hiranamibushan (10 years ago)

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RAKESH  (10 years ago)

let 2x+y+3=z
=> 2+dy/dx = dz/dx
=> dy/dx = (dz/dx -2)
so eqn becomes
dz/dx -2 = tan^2z
=> dz/dx= tan^2z+ 2
=> dz/(tan^2z +2)=dx
let tanz=k then sec^2zdz=dk => dz=dk/(1+k^2)
=> dk/(k^2+1)(k^2+2)=dx
=> [1/(k^2+1)-1/(k^2+2)]dk = dx
integrate => tan−1(k)- 1/sqrt(2)* tan-(k/sqrt2)=x
=> tan-(tan(2x+y+3))-tan-1(tan(2x+y+3)/sqrt2)=x
=> x+y+3-tan-1(tan(2x+y+3)/sqrt2)=0

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