Q. 225.0( 1 Vote )

Solve the followi

Answer :

Given: differential equation xdy – (y + 2x2) dx = 0


To find: the value of given differential equation


given: xdy – (y + 2x2) dx = 0


Dividing throughout by dx,



Dividing throughout by x we get,




This is of the of the standard form, i.e.,



Where and Q=2x


And we know the integrating factor is


IF=e∫P dx


Substituting the value of P in the IF, we get




But we know integration of is log x, substituting this in athe bove equation, we get


IF=e-log( x)


Or,



But elog x=x, so he above equation becomes,


IF=x-1



So the general solution of a differential equation is


y(IF)=∫(Q×I.F)dx+C


Substituting the corresponding values in the above equation, we get




On integrating, we get




Or


y=2x2+Cx


Hence this is the solution of the given differential equation


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