Q. 65.0( 1 Vote )

Solve the following differential equations:


Answer :

Given Differential equation is:




We know that 1–cos2x = sin2x


……(1)


Let us assume z = x– 2y


Differentiating w.r.t x on both sides we get,




……(2)


Substitute (2) in (1) we get,





Bringing like variables on same side (i.e., variable seperable technique) we get,



We know that


sec2zdz = dx


Integrating on both sides we get,


∫sec2zdz = ∫dx


We know that:


(1) ∫sec2xdx = tanx + C


(2) ∫adx = ax + C


tanz = x + C


Since z = x – 2y we substitute this,


tan(x–2y) = x + C


The solution for the given Differential Equation is tan(x–2y) = x + C.


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