Solve the differential equation -x-y-2- dx-2xy- dy- - 0-y-2-x- ln- ax- - 0y-2-y- ln- ax- - 0y-2-x- ln- ax- - 0y-2-y- ln- ax- - 0

Question

Toppr Admin · Accepted Answer

-x-x2212-y2-dx-2xydy-0-x21D2-2ydydx-x2212-y2x-x2212-1Substitute v-y2-x21D2-dv-2ydydvdx-x2212-vx-x2212-1 -xA0- -1-Here P-x2212-1x-x21D2-x222B-Pdx-x2212-x222B-1xdx-x2212-logx-log1x-x2234-I-F-elog1x-1xMultiplying -1- by I-F- we get1xdvdx-x2212-vx2-x2212-1xIntegrating both sides w-r-t x we getvx-x2212-x222B-1xdx-a-x2212-logx-a-x21D2-y2-xlogax

Solve the differential equation (x−y2)dx+2xydy=0.y2+xlnax=0y2−ylnax=0y2−xlnax=0y2+ylnax=0

(x−y2)dx+2xydy=0⇒2ydydx−y2x=−1Substitute v=y2⇒dv=2ydydvdx−vx=−1 ...(1)Here P=−1x⇒∫Pdx=−∫1xdx=−logx=log1x∴I.F.=elog1x=1xMultiplying (1) by I.F. we get1xdvdx−vx2=−1xIntegrating both sides w.r.t x we getvx=−∫1xdx+a=−logx+a⇒y2=xlogax

Solve the differential equation $(x - y^{2}) d x + 2 x y d y = 0$ .
$y^{2} + x l n a x = 0$
$y^{2} - y l n a x = 0$
$y^{2} - x l n a x = 0$
$y^{2} + y l n a x = 0$