Applied Mathematics 2270A/B Chapter Notes - Chapter 2.5: Yde

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samanthaadams765

9 Dec 2022

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Western University

Department

Applied Mathematics

Course

Applied Mathematics 2270A/B

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5 * using substitution to turn solvable ones unsolvable de to. Substitution (cid:8869) homogeneous a bernoull, is d = f (ax +by +c) * homogeneous a l l elements are of same degree set to. 0 in m14y)dxc+n(xy) dy = 6 can write as: 2022 +y2)dxc + (c22-xy) dy = 0 y = ux, dy= udx+xdu. 21+u?) dxc +(1-1) (ndxc + xdn) = 0 (1+ u2) deaf adxtecde-uidx-ux dow (i+ up +h-u/2) dxc+(cc-ux) dw = 0. 11+ n) dx +(cc-uxc) de = 0 (i + u) due t >cl- n) dw =0. W= 3kc example: expydxc + (2"+y") dy = 0 since term is. 3 = vg; dx= vdy +yde (ar3yt) (vdy +ydu) + (v4y + 34) dy = 0. >y4 are (vdytydu) + (04+1) dy = 0. 2 dy +avsydo+vtdy + by = 0 (204 + v4 +1) dy + 2v3y dv =d.

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Applied Mathematics 2270A/B Chapter Notes - Chapter 2.5: Yde

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