Q. 145.0( 3 Votes )

Solve the followi

Answer :


Given: differential equation x dy +(y – x 3) dx = 0


To find: the value given differential equation


given: x dy +(y – x 3) 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=x2


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 the above equation, we get


IF=elog( x)


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


IF=x


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




Hence this is the solution of the given differential equation


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