MATH 4B Lecture Notes - Lecture 3: Tangent Half-Angle Substitution, Tonne, Product Rule
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Define homogenous , inhomogeneous , and autonomous : autonomous : an equation is autonomous. It doesn"t if explicitly depend ont e. g . money . y y. "t homogenous : inhomogeneous : e. g . y. Analytic methods for linear & non-linear differential equations . an example of the weierstrass substitution y. Istahcylz ) ttc tf antan -11=912 y - zartan t - Qctsy "t petty = gets how to compute y. 2nd : y "t phy = got ) goal is to had ult so that witty "t ucttptttyutttgtt. I view as a single derivative dluuty ) : witty "t wut potty to be the. : adf. li#gctd--f"ctsgctitfctsbilt) d cutty ) ldcucttyl-futsgctsdtuttty-juttgtttdt. ge/ulttglhdtw choose w # =p # et mdt. = utttgttl d cutty ) result of product rule cuts = etpctsdt. =p # ult ) a first order linear eg . ty y. I test ty = not ,=elphdt= t e e-ty " e-ty-e-t. et-se-tj-e-ty-etdce-tyl-etdtldle-tyj. ge e" i etc tde y = ett cet.
