Systems of ODEs - Maple Help
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ODE Steps for Systems of ODEs

 

Overview

Examples

Overview

• 

This help page gives a few examples of using the command ODESteps to solve systems of ordinary differential equations.

• 

See Student[ODEs][ODESteps] for a general description of the command ODESteps and its calling sequence.

Examples

withStudent:-ODEs:

high_order_ode1diffyx,x,x,x+3diffyx,x,x+4diffyx,x+2yx=0

high_order_ode1ⅆ3ⅆx3yx+3ⅆ2ⅆx2yx+4ⅆⅆxyx+2yx=0

(1)

ODEStepshigh_order_ode1

Let's solveⅆ3ⅆx3yx+3ⅆ2ⅆx2yx+4ⅆⅆxyx+2yx=0Highest derivative means the order of the ODE is3ⅆ3ⅆx3yxCharacteristic polynomial of ODEr3+3r2+4r+2=0Roots of the characteristic polynomialr=−1,−1I,−1+ISolution fromr=−1y1x=ⅇxSolutions fromr=−1Iandr=−1+Iy2x=ⅇxsinx,y3x=ⅇxcosxGeneral solution of the ODEyx=c__1y1x+c__2y2x+c__3y3xSubstitute in solutions and simplifyyx=ⅇxc__1+c__2sinx+c__3cosx

(2)

macroY=y1x,y2x:

sys2diffY,x=`%.`Matrix7,1,`-`4,3,Y

sys2ⅆⅆxy1xⅆⅆxy2x=71−43·y1xy2x

(3)

ODEStepssys2

sys3diffY,x=Matrix1,2,3,2·Y+1,expx

sys3ⅆⅆxy1xⅆⅆxy2x=y1x+2y2x+13y1x+2y2x+ⅇx

(4)

ODEStepssys3

sys4diffwx,x=wx+2zx,diffzx,x=3wx+2zx+expx

sys4ⅆⅆxwx=wx+2zx,ⅆⅆxzx=3wx+2zx+ⅇx

(5)

ODEStepssys4

See Also

diff

Int

Student

Student[ODEs]

Student[ODEs][ODESteps]

 


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