Lecture 1 Notes

Y 0 method of integrating factors section 21 a

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Unformatted text preview: ue problems (IVP) • An initial condition is an added constraint on a solution. • e.g. Solve t 2 dy dt + 2ty (t) = sin(t) subject to the IC y (π ) = 0 . Initial conditions (IC) and initial value problems (IVP) • An initial condition is an added constraint on a solution. • e.g. Solve t 2 dy dt + 2ty (t) = sin(t) (A) (B) (C) (D) subject to the IC C + cos(π ) y (t) = − π2 1 − cos(t) y (t) = − t2 1 + cos(t) y (t) = t2 1 + cos(t) y (t) = − t2 y (π ) = 0 . Initial conditions (IC) and initial value problems (IVP) • An initial condition is an added constraint on a solution. • e.g. Solve t 2 dy dt + 2ty (t) = sin(t) (A) (B) (C) (D) subject to the IC C + cos(π ) y (t) = − π2 1 − cos(t) y (t) = − t2 1 + cos(t) y (t) = t2 1 + cos(t) y (t) = − t2 • An Initial Value Problem (IVP) is a ODE together with an IC. y (π ) = 0 . Method of integrating factors (Section 2.1) • A few examples - for each one, ﬁnd a function f(t) to multiply through by so that the left hand side becomes a product rule: Method of integrating factors (Section 2.1) • A few examples - for each one, ﬁnd a function f(t) to multiply through by so that the left hand side becomes a pr...
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