Class notes #1 for MTH G131: Fall 2008Linear first order ODE’sSuppose thatp(x), q(x) are continuous in theopen interval (a, b), andx0∈(a, b). Then there is a unique solutiony=g(x)of the linear ODEdydx+p(x)y=q(x),a < x < bsatisfyingg(x0) =y0for any real numbery0.Existence and uniqueness for first order ODE’sConsider the InitialValue Problemdydx=f(x, y),y(x0) =y0Supposefand∂f∂yare continuous in some rectangleα < x < β,γ < y < δcontaining (x0, y0). Then in some intervalx0-h < x < x0+hcontained
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