Linear First Order DE Recipe - Handwritten Notes | MAT 2705, Study notes of Differential Equations

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linear frstorder DE renee: a linear DE depends on the unienawn and rhs derivates linearly oO recognize and put in new standard form : Wy berms only on LAS a! ante ters oy EXAMPLE ¥ Bike dy, PG) y = Ax) -xt = g [ See POY é"| Bake = 3x | ise] @ $ Poa ecu) (-tedves 2 den, @ SPpidadx exponentiate to get en u \ntegrahing, fackur " =x —x2 BPbddx e* Bh~tnj) = Bxe @: es hina dy 4 pbdy = bre eet Ge § [ee = xe*} a yer = laxe™ dx = ~3f © (-axdeo) Le @ = a (ye Seen) menoRIZE | % Use product rule . Spbady " MAK @5 [ d (yeSh™) = Gre |e inkegrake = 3 Geta Spbadx Spoyax pu = get ec = \ame ay + C = - ye 5 solve ~ ~2e Mec @ y= re [ S069 estas + c| 2 _ . y= eee" ec] = done! Csitagtify!) 2 = 3. ok gxce