# Calculus

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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.

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