# Calculus

posted by
**COFFEE**
.

Given the differential equation:

dy/dx = y(1+x), y(0)=1,

Use Euler's method with step size .1 to approximate y(.3).

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

Is this the answer or am I going about this the wrong way? If so, please steer me in the right direction. Thanks.