Troubleshooting Derive 6 for a BV Problem

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SUMMARY

The discussion centers on troubleshooting the Derive 6 software for solving a boundary value problem represented by the differential equation d²y/dx² + 8dy/dx + 16y = (4e^{-4x})(sinx+cosx)² with initial conditions y(0)=y'(0)=0. The user attempted to use the DSOLVE2_BV function but did not obtain the correct solution. It was suggested that while solving by hand is possible using the method of variation of parameters, the integrals involved can be complex. The user is specifically utilizing Derive 6 for computational assistance.

PREREQUISITES
  • Understanding of boundary value problems in differential equations
  • Familiarity with the method of variation of parameters
  • Knowledge of the Derive 6 software and its functions
  • Basic skills in solving differential equations
NEXT STEPS
  • Research the method of variation of parameters for solving differential equations
  • Explore advanced features of Derive 6, particularly DSOLVE2_BV
  • Learn about numerical methods for boundary value problems
  • Study the integration techniques required for complex integrals in differential equations
USEFUL FOR

Mathematicians, engineering students, and anyone working with differential equations and boundary value problems, particularly those using Derive 6 for computational solutions.

gtfitzpatrick
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i'm not sure if this is the right place but I'm trying to get my head around derive 6 and i have a couple of questions that don't seem to be coming out right...

d[tex]^{2}[/tex]y/dx[tex]^{2}[/tex] + 8dy/dx + 16y = (4e[tex]^{-4x}[/tex])(sinx+cosx)[tex]^{2}[/tex] ; y(0)=y'(0)=0


so i inputed DSOLVE2_BV(8, 16, (4·^(- 4·x))·(SIN(x) + COS(x)) ∧ 2, x, 0, 0)

but its not throwing up the right answer?
 
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Are you doing this by hand or computer? If you're solving it by hand, note that the variation of parameters works here; only problem is that the integrals you have to solve for the particular solutions can be rather difficult, though doable.
 
trying by computer, using a program called derive
 

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