ODE Steps for Systems of ODEs with IVP
Overview
Examples
This help page gives a few examples of using the command ODESteps to solve systems of ordinary differential equations with initial values.
See Student[ODEs][ODESteps] for a general description of the command ODESteps and its calling sequence.
withStudent:-ODEs:
high_order_ivp1≔diffyx,x,x,x+3diffyx,x,x+4diffyx,x+2yx=0,evaldiffyx,x,x=0=−1,evaldiffyx,x,x,x=0=2,y0=1
high_order_ivp1≔ⅆ3ⅆx3yx+3ⅆ2ⅆx2yx+4ⅆⅆxyx+2yx=0,ⅆ2ⅆx2yxx=0|ⅆ2ⅆx2yxx=0=2,ⅆⅆxyxx=0|ⅆⅆxyxx=0=−1,y0=1
ODEStepshigh_order_ivp1
macroY=y1x,y2x:
ivpsys2≔diffY,x=`%.`Matrix7,1,`-`4,3,Y,evalY,x=0=1,1
ivpsys2≔ⅆⅆxy1xⅆⅆxy2x=71−43·y1xy2x,y10y20=11
ODEStepsivpsys2
ivpsys3≔diffY,x=Matrix1,2,3,2·Y+1,expx,evalY,x=1=0,−1
ivpsys3≔ⅆⅆxy1xⅆⅆxy2x=y1x+2y2x+13y1x+2y2x+ⅇx,y11y21=0−1
ODEStepsivpsys3
ivpsys4≔diffwx,x=wx+2zx,diffzx,x=3wx+2zx+expx,w−1=2,z−1=−2
ivpsys4≔ⅆⅆxwx=wx+2zx,ⅆⅆxzx=3wx+2zx+ⅇx,w−1=2,z−1=−2
ODEStepsivpsys4
See Also
diff
Int
Student
Student[ODEs]
Student[ODEs][ODESteps]
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