Solving Linear ODEs - Maple Help

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Solving Linear ODEs

Description

• 

The general form of a first order linear ODE is given by the following:

linear_ode := diff(y(x),x)+f(x)*y(x)-g(x);

linear_ode:=ⅆⅆxyx+fxyxgx

(1)
  

where f(x) and g(x) are arbitrary functions. See Differentialgleichungen, by E. Kamke, p. 16. This type of ODE can be solved in a general manner by dsolve as follows:

Examples

withDEtools,odeadvisor

odeadvisor

(2)

odeadvisorlinear_ode

_linear

(3)

dsolvelinear_ode

yx=∫gxⅇ∫fxⅆxⅆx+_C1ⅇ∫fxⅆx

(4)

See Also

DEtools, odeadvisor, dsolve, and ?odeadvisor,<TYPE> where <TYPE> is one of: quadrature, linear, separable, Bernoulli, exact, homogeneous, homogeneousB, homogeneousC, homogeneousD, homogeneousG, Chini, Riccati, Abel, Abel2A, Abel2C, rational, Clairaut, dAlembert, sym_implicit, patterns; for other differential orders see odeadvisor,types.


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