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𝑑𝑡

= −𝑎 ⋅ 𝐵, 𝐴 0 = 𝐴

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𝑑𝐵

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= −𝑏 ⋅ 𝐴, 𝐵 0 = 𝐵

, 𝐵 > 0!

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𝑑𝐴

𝑑𝑡

= −𝑎 ⋅ 𝐵 ⋅ 𝐴, 𝐴 0 = 𝐴

, 𝐴 > 0!

𝑑𝐵

𝑑𝑡

= −𝑏 ⋅ 𝐴 ⋅ 𝐵, 𝐵 0 = 𝐵

, 𝐵 > 0!

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𝑑𝐴

𝑑𝑡

= −𝑎 ⋅ 𝐵, 𝐴 0 = 𝐴

, 𝐴 > 0 !

𝑑𝐵

𝑑𝑡

= −𝑏 ⋅ 𝐴, 𝐵 0 = 𝐵

, 𝐵 > 0!

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𝑔 𝑡 = 𝑦

+ 𝑓

(𝑥)𝑦

+ 𝑓

𝑥 𝑦, 𝑔 𝑡 = 0!

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()!92,%-',-()!2A!$99(!)((66(!71,9-$2,();!.$A,$,A(),(!9'64(%!4$77()(,-$'66$A,$,A()!' 7!T;!2)4(,3!4'!

4()! $,4AZ)! :DD3! '6 - %Z! (,! -2! A',A(! 4$77()(,-$()(-! 71,9-$2,;! B()! 7$,4(%! #()! $99(! 72)+6()! -$6! '-!

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

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922)4$,'-%:%-(+!2A!4()+(4!6W%(!6$A,$,A(,!,1+()$%9;!.$,Q((6(+(,-(-!8(%-Z)!'7!-)(!%-W))(6%()?!

3!:

!2A!'!2A!2&%9)$M(%!%Z6(4(%?!(𝑥

, 𝑦

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!2A!:

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3!:

F3!2A!'!()!14-):9!

72)!(,!#X64,$,A!$!4(-!&1,9-;!C-!6$,Q((6(+(,-!()!(-!6$66(!-',A(,-%-:99(3!4()!M$%()!#X64,$,A(,!$!

4(-! A$M,(! &1,9-! 72)! (,! 6W%,$,A%91)M(3! 4()! ,(-2&! AZ)! A(,,(+! 4(-! &1,9-;! e4)(A,()! +',! '66(!

6$,Q((6(+(,-()! $! (-! 8(%-(+-! $,-()M'6! $,4(,! 72)!(-! A)'7M$,41(3! M$6! +',! 91,,(!%(! #X64,$,A()! $!

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#X64,$,A%7(6-;! h()1,4()! 7W6A()! (-! (9%(+&(6! &Z! 14)(A,$,A! '7! (-! (,9(6-! 6$,Q((6(+(,-! 72)!

6$A,$,A(,?!

𝑑𝑦

𝑑𝑡

= −

⋅ 𝑡 ⋅ 𝑦!

R$!9',!6'4(!#WQ)(!%$4(!'7!6$A,$,A(,!9 '64(!%E-3!:F3!'6-%Z!(,!71,9-$2,!%3!4()!'7#X,A()!'7!-!2A!:;!

𝑑𝑦

𝑑𝑡

= 𝑠(𝑡, 𝑦)!

hM$%! (,! 6W%,$,A! -$6! 4$77()(,-$'66$A,$,A(,! AZ)! $A(,,(+! &1,9-(-! E-

F3! M$6 ! -',A(,-(,! -$6! 4(,,(!

6W%,$,A%91)M(!$!4(-!A$M,(!&1,9 - !#'M(!#X64,$,A%92(77$/$(,-(,!'m%E-

F3!4'!

!()!(-!14-):9!72)!

-',A(,-#X64,$,A(,;!R$!7$,4()!(-!6$,Q((6(+(,-!$!&1,9-(-!ET3TF?!!

𝑎 =

𝑑𝑦

𝑑𝑥

= −

⋅ 2 ⋅ 2 = −2!

!@2A!ELF!O!U)$%-(,%(,3!C)$9!l!B$77()(,-$'66$A,$,A()!E%;!kS3!6;!TJF!

!@2A!EjF!O![$(6%!h;!.')%(,!O!g'4%!+'-(+'-$9!E%;!HK!6;!JJF!

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JV!

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#X64,$,A%7(6-3!2A!-$6+(4!7Z!(,!,1+()$%9!6W%,$,A!A(,,(+!&1,9-(-!ET3TF?!!

B(!+',A(!6$,Q((6(+(,-()3!4()!()!&62--(-!+(4!(-!$,-()M'6!&Z!/';!T!$!922)4$,'-%:%-(+(-3!A$M()!(-!

A24-!M$%1(6-! 8$66(4(!'73!#M2)4',! 4(!1(,4(6$A-! +',A(!6W%,$,A%91)M()! %()!14! 72)!4(! 72)%9(66$A(!

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,WQ'A-$A! 4(,! 6W%,$,A3! 4()! AZ)! A(,,(+! 4(-! &1,9-3! %2+! %-')-8(-$,A(6%(,! ',%6Z)3! '6-%Z! (,!

&')-$916X)! 6W%,$,A;! B(,! )W4(! A)'7! M$%()! 4(,! 6W%,$,A! -$6! 6$A,$,A(,! !

= −

⋅ 𝑡 ⋅ 𝑦!3! 4()! AZ)!

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@E-F;!B(--(!M$6!A$M(!(-!2M()86$9!2M()!6W%,$,A(),(!72)!4(!9286(4(!4$77()(,-$'66$A,$,A();!C-!%Z4',-!

#X64,$,A%7(6-!9'64(%!(-!7'%(&62-; !_',!9',!$+$46()-$4!14%9$7-(!-',A(,-(,!$!6$,Q((6(+(,-(-!+(4!

M(9-2)()3! #M$69(-! A$M()! (,! 8(4)(! 72)%-Z(6%(! 72)3! #M$69(,! )(-,$,A! A)'7(,! 8(MXA()! %$A3! ,Z)! -!

X,4)(%;!N'%(&62--(-!4(+2,%-)()(-!$!Y;T;!

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7W)%-(!2)4(,3!9',!'6-%Z!$99(!6W%(%!#M()!72)!%$A3!72)4$!4(!#')!,2A(-!+(4!#$,',4(,!'-!AW)(;!R$!%()!

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bORUQWYP[R)P`T\Q\X)QXN\\N_)bY\WUNU)L+F+M)

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𝑑𝐴

𝑑𝑡

= −𝑏 ⋅ 𝐵, 𝐴 0 = 𝐴

𝑑𝐵

𝑑𝑡

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𝑑𝐴

𝑑𝑡

= −10 ⋅ 𝐵(𝑡 ), 𝐴 0 = 34000!

𝑑𝐵

𝑑𝑡

= −𝐴(𝑡), 𝐵 0 = 7800!

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?!𝑔 𝑥 = 𝑘 ⋅ 𝑓 𝑥 →

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𝑑

𝐴

𝑑𝑡

= −10 ⋅ −𝐴 𝑡 →

𝑑

𝐴

𝑑𝑡

= 10 ⋅ 𝐴 𝑡 !

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Fundet*på:*http://www.eyewitnesstohistory.com/pfdday2.htm*