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How to solve ODEs PDEs See Guess u 1 x x f0= cf f= (( 1)(k 1 cx)) 1 1 y0 P(x)y= Q(x) y= F(x) 1 R x Q(t)F(t)d tCF(x) 1F(x) = exp R x P(s)d s G = 1 Subin H= G 1= multiply by G =1 too Backwards SDE Let ˘so E(˘). C { E u b N X Y E G F ^ G N o ŎЁF O N s i ~ L n E X j { ̉ i F6 ~ { Ԃ ́A ܂ꂽ u Ԃ 疾 邢  Ȃǂ 킩 邭 炢 ɁA o B Ă ܂ B Ă R A S قǂ A G { ߂ Č Ă ܂ 傤 B l ̊ ⌴ F ̂͂ 肵 ̂Ȃǂ Ƃ݂ A ڂŒǂ 悤 ɂȂ Ă ܂ B ʉ ̂₳ ^ b ` ƁA R g X g ̂͂ 肵 G ̃C X g A ͂ ߂ĊG { ɏo Ԃ ɂ҂ B ` t R ⓮ Ȃ̂őً ɂ ߁B. Y= u ss 2u st u y=u ss y u tt y= u s u yy=u sss y u stt y= u ss Substituting these expressions into the given equation we nd u ss u tt= 0 Problem 14 For each of the following PDEs, state its order and whether it is linear or nonlinear If it is linear, also state whether it is homogeneous or nonhomogeneous (a) uu x x2u yyy sinx= 0 (b) u.
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