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+// example 6.15
+//caption: solving ODE by tailor series method
+// u'=t^2+ u^2,  u0=0;
+
+t=0;U=0;                   //at t=0, the value of u is 0
+U1=0;                  // u1 is the 1st derivatove of the funtion u 
+U2=2*t+2*U*U1                // U2 ---- 2nd derivative
+U3=2+2*(U*U2+U1^2)
+U4=2*(U*U3+3*U1*U2)
+U5=2*(U*U4+4*U1*U3+3*U2^2)
+U6=2*(U*U5+5*U1*U4+10*U2*U3)
+U7=2*(U*U6+6*U1*U5+15*U2*U4+10*U3^2)
+U8=0;
+U9=0;
+U10=0;
+U11=2*(U*U10+10*U1*U9+45*U2*U8+120*U3*U7+210*U4*U6+126*U5^2)
+                                 // U11 is the 11th derivative of u
+
+
+taylor(1)                             
+\ No newline at end of file