1. y0=3, y1=3+3x, y2=3+3x+32x2, y3=3+3x+32x2+12x3, y4=3+3x+32x2+12x3+18x4; y(x)=3ex
3. y0=1, y1=1−x2, y2=1−x2+12x4, y3=1−x2+12x4−16x6, y4=1−x2+12x4−16x6+124x8; y(x)=exp(−x2)
5. y0=0, y1=2x, y2=2x+2x2, y3=2x+2x2+43x3, y4=2x+2x2+43x3+23x4; y(x)=e2x−1
7. y0=0, y1=x2, y2=x2+12x4, y3=x2+12x4+16x6, y4=x2+12x4+16x6+124x8; y(x)=exp(x2)−1
9. y0=1, y1=(1+x)+12x2, y2=(1+x+x2)+16x3, y3=(1+x+x2+13x3)+124x4; y(x)=2ex−1−x=1+x+x2+13x3+⋯
11. y0=1, y1=1+x, y2=(1+x+x2)+13x3, y3=(1+x+x2+x3)+23x4+13x5+19x6+163x7; y(x)=11−x=1+x+x2+x3+x4+x5+⋯
12. y0=1, y1=1+12x, y2=1+12x+38x3+18x3+164x4, y3=1+12x+38x2+516x3+1364x4+⋯; y(x)=(1−x)−1/2
13. [x0y0]=[1−1], [x1y1]=[1+3t−1+3t],[x2y2]=[1+3t+12t2−1+5t−12t2],[x3y3]=[1+3t+12t2+13t3−1+5t−12t2+56t3]
14. x(t)=[et+tetet]
16. y3(1)≈0.350185