Solving Clairaut ODEs
Description
Examples
The general form of Clairaut's ODE is given by:
Clairaut_ode := y(x)=x*diff(y(x),x)+g(diff(y(x),x));
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);
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.
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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