Question

Find an integrating factor for (2xy^2)dx + (2x^2y+x^2y^2)dy = 0

Answer 1

zxyz da +(22y + xy) dy =0 (1) comparting (1) with Mart Ndy=0*2)- We get M = zuyu and N= 2xy + xyr. a = any, en la = Any + zay. = 2mg ( 1 ay zmyu - Ayy) =1.. y (3)

let u be an integrating factor of the equation (2) so, Cum de fuN) dy zo is an exact differential equation. Hence, the condition (um) = CUN) must be satisfied.

:: MONTM 2M = Men + NOU This gives , -M 34 + N + y a to co a function of u is that au Now, suppose y only , so OC Then (4) gives >(5) Dotas siguiente from (3) & (5) , we get . ū =lidy . MCA :. Integrating factor be e.

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