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Sx cxg fuc. Uxy = f′(x)g′(y) Substituting into the PDE, we have uuxy = f(x)g(y)f′(x)g′(y) = uxuy Hence, u(x,y) = f(x)g(y) is a solution of the PDE 3 Boundary value problem The Poisson’s Equation is the nonhomogeneous version of Laplace’s Equation ∂2u ∂x2 ∂2u ∂y2 = ρ(x,y) (1) Assume that ρ(x,y) = 1 (a) Find the condition under. } \ ȂǃX c C x g p X ^ b t x X g1,270 ~ Ƀ S f U C Ȃǖ v g B w ɒʋC ̂悢 b V f ނ g p B T C YM `XXL B J 10 F y ܂Ƃߔ 30,000 ~( ŕ ) ȏ ő z. False because on integrating the x terms will be the same but the constant may differ so when f'(x)=g'(x) then f(x) is not equal to g(x) always.

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C x g p x X g1 1,0 ~ Ƀ` E Ѓ S Ȃǖ v g B T C YL `3L B J 9 F B y ܂Ƃߔ 30,000 ~( ŕ ) ȏ ő T r X z f B X i ʐ^ j g 158cm E 395cm E o X gcm E E G X g59cm E q b v85cm ł B. Blender 2D X L Ƀv X B l ȃf W ^ \ Ől X 𖣗 B w Z f U C i w @ ̃f W ^ C X g U ̏ڍׂɂ Čf ڂ Ă ܂ B( s c ). Since the fi’s are linearly independent one concludes that β = 0;.

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We use formula 71 in the table of integral formulas to evaluate ∫ sinh (x) dx and integral of the constant 3 to obtain ∫ (sinh (x) 3) dx = cosh (x) 3 x c 4 The integrand is the product of two function x and sin (x) and we try to use integration by parts in rule 6 as follows Let f(x) = x , g'(x) = sin(x) and therefore g(x) = cos(x). S f U C A V { } N A C X g 𒆐S ɁA f W ^ i ̌ J Ă ܂ B d ̂ ˗ ҂ Ă ܂ B Q l i \ i S f U C j E _ ^ T v R _ 񎦁A1 _ I C. F U C T V c ̒ʔ̃T C g A O j t I C X g A ł B Y A f B X A L b Y ܂ŁA C X g A S A t H g A O t B b N A R W Ȃǂ̑ ʂȃf U C T V c ̔ Ă ܂ B.

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