Linear of Order One differential equations sample problems, Lecture notes of Differential Equations

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“EINEAR EQUATION OF ORDER ONE Sa TS gy, 2 AK (se + POY = ACK) SOLUTION * fal ‘ use @°) “ag Integrating factor . then , {Pax ou + Pe Fre = aeis™ multiply by i ’ Pd Say tay t Ped = eax Let : u= fFdx du= Pdx thus , e"dy + ye'du = Ge but > d(ety) = edy eyetan And so, ace’y) = a ea, face’y) = fae dx $c e’y 2 fae” y, tc but > u=JPdx GENERAL EQUATION . ye! Pax = fae! 4x +e J Fang EXERCISES | u x5 + 3y dy — xdY =O) 4 : } yx? = fate + Cfo divide by-%dx , no ~ 28439 4 DY LG . uxeafxdx + F x dx / abey 2 = 2 ay 1, Ux = 2 4E TY dy 3 ~ ye 2 2 J de 7 XE O_ . 3 j 7 multiply by 2x", 2-2 wy = x4 : 2g s x8 $x? ans, Pox) 2-3 : a@es x4 2, 2(2xy + 4y~-3)dx . + («42)7dy =O For Integrating factor : ef Pade fo $ax 2 [ay (x42) -3] + (xt 2)"dyz0 = en divide by (xt2)?dx 4 apn? af2y x42)-3] | oY 2 9 pi Pax = <3 (x +2)? ax thus, du , [4 ]y -S.2 i elronen facts yc axt faalY Gry ° 51 bef} CamScanner