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different solutions NDSolve/ DSolve

  • To: mathgroup at smc.vnet.net
  • Subject: [mg126977] different solutions NDSolve/ DSolve
  • From: Narasimham <mathma18 at hotmail.com>
  • Date: Thu, 21 Jun 2012 05:20:33 -0400 (EDT)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com

Not able to find error in the closed form solutions. Integration
Conditions or arguments may need to be changed. Please help

Regards
Narasimham

Clear[tmax];
DSolve[Z'[t]==Sqrt[(tmax^2-t^2)/(t^2+1)],Z,t]
tmax=2.
gclosed=Plot[tmax*EllipticE[ArcSinh[t],-(1/tmax^2)],{t,0,tmax}] ;
gTrigHyp=Plot[tmax*EllipticE[ArcSin[t],-(1/tmax^2)],{t,0,tmax}] ;
NDSolve[{Z'[t]==Sqrt[(tmax^2-t^2)/(t^2+1)],Z[0]==0},Z,{t,0,tmax}];
z[t_]=Z[t]/.First[%];gnumeric=Plot[z[t],{t,0,tmax}, PlotStyle-
>{Red,Thick}] ;
Show[gclosed,gTrigHyp,gnumeric]



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