Solving Clairaut ODEs - Maple Programming Help

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Solving Clairaut ODEs

 

Description

Examples

Description

• 

The general form of Clairaut's ODE is given by:

Clairaut_ode := y(x)=x*diff(y(x),x)+g(diff(y(x),x));

Clairaut_ode:=yx=xⅆⅆxyx+gⅆⅆxyx

(1)
  

where g is an arbitrary function of dy/dx. See Differentialgleichungen, by E. Kamke, p. 31. This type of equation always has a linear solution:

y(x) = _C1*x + g(_C1);

yx=_C1x+g_C1

(2)
• 

It is also worth mentioning that singular nonlinear solutions can be obtained by looking for a solution in parametric form. For more information, see odeadvisor/parametric.

Examples

withDEtools,odeadvisor

odeadvisor

(3)

odeadvisorClairaut_ode

_Clairaut

(4)

odeyx=xⅆⅆxyx+cosⅆⅆxyx

ode:=yx=xⅆⅆxyx+cosⅆⅆxyx

(5)

ansdsolveode

ans:=yx=arcsinxx+x2+1,yx=_C1x+cos_C1

(6)

Note the absence of integration constant _C in the singular solution present in the above.

See Also

DEtools

odeadvisor

dsolve

quadrature

linear

separable

Bernoulli

exact

homogeneous

homogeneousB

homogeneousC

homogeneousD

homogeneousG

Chini

Riccati

Abel

Abel2A

Abel2C

rational

Clairaut

dAlembert

sym_implicit

patterns

odeadvisor,types

 


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