Given the differential equation:

Question

dy/dx = y(1+x), y(0)=1,
Use Euler's method with step size .1 to approximate y(.3).

... please check this for me! no one has responded to this question yet.. thanks.

y' = y(1+x), y'(0) = 1(1+0)=1
->the solution has slope 1 at the point
(0,1); x0=0, y0=1, h=0.1, F(x,y)=y(1+x)

y1=y0+h*F(x0,y0)
y1=1 + 0.1(1(1+0))
y1=1.01

y2=1.01 + 0.1(1.01(1+0.1))
y2=1.02111

y3=1.02111 + 0.1(1.02111(1+0.2))
y3=1.1436432