Q. 185.0( 1 Vote )

Show that the dif

Answer :

Given, We have a differential equation,

To Find: Prove that it is a homogenous differential equation and solve.


Explanation: We have


It can be written as



Now, to prove that it is a Homogenous differential equation, we put x = λx and y = λy then



Now, Taking λ as common from both numerator and denominator, we get



If, then it is an homogenous differential equation


Now, Solution of this differential equation is


Put y = v x


Then,



So, When we compare this derivative from the given equation we get



Taking x as common from R.H.S








On integrating both sides,



For Solving L.H.S


Put v2 + v + 1 = t


2v + 1 dv = dt


So,








Now, Put the value of v = y/ x, we get






Hence, This is the solution of Given differential equation.


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