For with , approximate by taking two successive steps: (i) a step of from to ,…

MATHEMATICS · Subjective · AP · Calculus BC · Differential Equations · Differential Equations

Problem

For

\dfrac{dy}{dx}=x^{2}-y

with

y(0.10)=0.50

, approximate

y(0.25)

by taking two successive steps: (i) a step of

\Delta x=0.10

from

x=0.10

x=0.20

, followed by (ii) a step of

\Delta x=0.05

from

x=0.20

x=0.25

. Give the final numerical approximation of

y(0.25)