MATHEMATICS · Subjective · AP · Calculus BC · Differential Equations · Differential Equations
Problem
An initial–value problem satisfies dxdy=xy+1 with y(0)=0. Begin at x0=0 with step size h0=0.20. After each move, compute the slope at the new point; if its magnitude exceeds 1, set the next step size to half the current step size, otherwise leave the step size unchanged. Continue taking steps until you first reach or pass x=0.35, adjusting the final step so that you land exactly on x=0.35. Provide the numerical approximation for y(0.35), rounded to three decimal places.