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2023年12月8日 星期五

112年高科大碩士班-工程數學詳解

 




解答{A(6,10,4)B(4,6,2)C(2,2,8){AB=(2,4,2)AC=(8,12,4)n=AB×AC=(40,24,8):40(x6)+24(y10)8(z4)=05x3y+z=4ABC=12n=12402+242+82=435
解答y+y=2u(tπ)2u(t2π)L{y}+L{y}=2L{u(tπ)}2L{u(t2π)}s2Y(s)sy(0)y(0)+Y(s)=2s(eπse2πs)(s2+1)Y(s)=2s(eπse2πs)+1Y(s)=2s(s2+1)(eπse2πs)+1s2+1y(t)=L1{Y(s)}y(t)=2u(tπ)(1cos(tπ))2u(t2π)(1cos(t2π))+sin(t)
解答y4y+4y=(24x212x)e2x=r(x)y4y+4y=0yh=c1e2x+c2xe2x{y1=e2xy2=xe2xW(y1,y2)=|y1y2y1y2|=e4xyp=y1y2rwdx+y2y1rwdx=e2x24x312x2dx+xe2x24x212xdx=2x4e2x2x3e2xy=yh+ypy=c1e2x+c2xe2x+2x4e2x2x3e2x





解答{M(x,y)=(x+y)2N(x,y)=2xy+x21My=2x+2y=Nx(exact)Φ(x,y)=(x+y)2dx=(2xy+x21)dy13x3+x2y+xy2+ϕ(y)=xy2+x2yy+ρ(x){ϕ(y)=yρ(x)=x3/3Φ(x,y)=13x3+x2y+xy2y+c1=0y(1)=213+2+42+c1=0c1=13313x3+x2y+xy2y=133

解答[423100420010120001]R1+R2R2,R1/4+R3R3[42310000311003/23/41/401]R1/4,R2/(3),2R3/3[11/23/41/4000011/31/30011/21/602/3]R3/2+R1R1,R2/2+R3R3[1011/301/30011/31/3001001/62/3]R2+R1R1[10001/31/30011/31/3001001/62/3]R2R3[10001/31/301001/62/30011/31/30]A1=[01/31/301/62/31/31/30]



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