Find the general solution of the differential equations `sec^2xtany dx – InterviewSolution

InterviewSolution

1.	Find the general solution of the differential equations `sec^2xtany dx+sec^2ytanx dy=0`
Answer» Correct Answer - `tan y = C (1-e^(x))` `int (sec^(2)x)/(tanx) dx +int (sec^(2)y)/(tany) dy = log \|C_(1)\|rArr log \|tanx\|+log \|tan y\| = log \|C_(1)\|` `therefore log \|tan x tany\| = log \|C_(1)\| rArr \|tan x tany\|=\|C_(1)\|.` `therefore tanx tan y = pm C_(1) = C.`

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))`