Given 1st order ODE, $ \frac{dy}{dx} =x+y, \ y_{0}=1 $, solve by picard's method using $y_{0}(x)= \cos x $ as initial approximation. $$ $$ I don't know how to start picard's method if the initial approximation is not constant. Can anyone just start the process.Please help me
picard's method
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$\begingroup$
ordinary-differential-equations
1 Answers
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Compute $$ y_1(x)=1+\int_0^xf(s,y_0(s))\,ds=1+\int_0^x(s+\cos s)\,ds $$ etc.