Find the general solution of each of the following differential equati – InterviewSolution

InterviewSolution

1.	Find the general solution of each of the following differential equations: `(dy)/(dx)=(1-cos x)/(1+cosx)`
Answer» Correct Answer - `y=2 "tan"(x)/(2)-x+C` `(dy)/(dx)=(1-cosx)/(1+cosx)=(2sin^(2)(x//2))/(2cos^(2)(x//2))="tan"^(2)(x)/(2)=("sec"^(2)(x)/(2)-1)` ` therefore int dy = int ("sec"^(2)(x)/(2)-1)dx.`

Discussion

No Comment Found

Related InterviewSolutions

For each of the folowing differential equations, find a particular solution satisfying the given condition: `(dy)/(dx) =-4xy^(2)," it being given that " y = 1 " when " x = 0.`
Find the general solution of each of the following differential equations: `(dy)/(dx)=(1-cos x)/(1+cosx)`
Find the general solution of each of the following differential equations: `(1)/(x)*(dy)/(dx)=tan^(-1)x`
Find the general solution of each of the following differential equations: `ydx +(1+x^(2))tan^(-1)xdy =0`
Find the general solution of the differential equations `sec^2xtany dx+sec^2ytanx dy=0`
Find the general solution of each of the following differential equations: `(dy)/(dx) = sin^(3)x cos^(2)x+xe^(x)`
Find the general solution of each of the following differential equations: `(dy)/(dx)+sin(x+y)=sin(x-y)`
Find the general solution of each of the following differential equations: `sin^(3)xdx -siny dy =0`
Find the general solution of each of the following differential equations: `(1)/(x)cos^(2)y dy +(1)/(y)cos^(2)xdx=0`
Find the general solution of each of the following differential equations: `(dy)/(dx)=(1+x^(2))(1+y^(2))`