'DIFFSIMPEQNS.TXT=TEST EQNS for MERGING with DIFFSIMP.Remove the ' from
'left END of each LINE AS needed.

'10PI=3.141592#:F=(PI*SIN(5*X(0,0))/8-EXP(PI*SQR(X(0,0)+1)/8)+SQR(X(O,O)+PI*5/8))*SQR(1+PI*(X(0,0)-1)^2/8)/((EXP(-1*X(0,0)*X(0,0))-PI/4)*(1+PI*(X(0,0)+1)^2/8))+PI/8:RETURN:' 1 ALG TRANSCENDENTAL:C=-1:X=-.716398

'10 F=2*X(0,0)-3*X(1,0)-17:RETURN:' 2 ALG LINS:C=0,0:Xo=4,X1=-3
'11 F=X(0,0)+X(1,0)-1:RETURN

'10 F=X(0,0)^2+X(0,0)*X(1,0)+X(1,0)^2-3:RETURN: ' 2  ALG TRANSCENDENTALS:C=0,0 :Xo=1.999,1.0636: X1=-.9537,.93459
'11F=SIN(X(0,0))-X(1,0)^2:RETURN

'10F=X(0,1)-X(0,0)-T:RETURN:' 1st ORDER: C(J)=0:X=EXP T-T-1:X=.718281828 @T=1
'10 F=X(0,5)-X(0,1)-1:RETURN:' 5th ORDER:C(J)=0,0,1,1,1 :X=EXP T-T-1=.718281828 @T=1

'10 F=X(0,2)-X(1,0)+T*T+1:RETURN: '2nd+0th ORDER NONLIN:C=1,1 for 2nd order,0 for 0th order.:Xo=EXP T;X1=EXP T+T^2+1
'11 F=X(1,0)-X(0,0)-X(0,0)/X(0,1)+T*T-2*(LOG(X(0,0)))^2:RETURN

'10F=X(0,2)-SQR((2+X(1,0)*X(0,1))/8):RETURN:' CATENARY,2nd+1st ORDER NONLINS: C(J)=2,0 for 2nd order,0 for 1st order.
'11 F=X(1,1)-SQR(1+X(0,1)^2):RETURN:'Xo=EXP T/2+EXP-T/2=2.255252 ;X1=EXP T/2-EXP-T/2=1.042191 @T=1

'10 F=X(0,2)-2*X(1,0)+5*X(0,0):RETURN:'  2 SPRINGS, 2 2nd ORDER LINS: C(J)=5,0,0,0 :Xo=4 C0S[T SQR 6]+COS T=-2.539321 @T=1
'11 F=X(1,2)-2*X(0,0)+2*X(1,0):RETURN:'                                         X1=-2 C0S[T SQR 6]+2 COS T=2.620416

'10 F=X(0,2)-X(0,0)*X(1,1)^2+2/X(0,0)^2:RETURN:' ORBITS, 2 2nd ORDER NONLIN :C=3,0,0,.333333: Xo=9/[2+COS X1]
'11 F=X(1,2)+2*X(0,1)*X(1,1)/X(0,0):RETURN

'10 GOSUB 740:F=X(0,2)-SIN((X(0,2)-(1+T)*SIN(T))/X(0,0)):RETURN:' IMPLICIT SIN, 2nd ORDER :C(J)=0,-1: X=-SIN T=-.8414709848 @T=1
'740IF X(0,0)=0 THEN X(0,0)=.1
'742RETURN

'10GOSUB 740:F=LOG(X(0,2))-(X(0,2)^2*LOG(X(0,0))+T*EXP(2*T))/(2*X(0,1)^2):RETURN:' IMPLICIT EXP, 2nd ORDER :C(J)=1,1: X=EXP T=2.718281828@T=1
 '740IF X(0,1)=0 THEN X(0,1)=.1
 '741IF X(0,2)<.1 THEN X(0,2)=.1
 '742IF X(0,0)<.1 THEN X(0,0)=.1
'743RETURN
                   DIFFSIMP TEST EQUATIONS: MACINTOSH LISTING