Q. 75.0( 1 Vote )

Solve the following differential equations:


Answer :

Given Differential Equation is:


……(1)


Let us assume z = x + y


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




……(2)


Substituting (2) in (1) we get,




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



We know that




We know that cos2z = cos2z – sin2z = 2cos2z – 1





We know that 1 + tan2x = sec2x




Integrating on both sides we get,



We know that:


(1) ∫sec2xdx = tanx + C


(2) ∫adx = ax + C



Since z = x + y, we substitute this,





the solution for the given differential equation is .


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