Solving ODEs That Are in Quadrature Format
Description
Examples
An ODE is said to be in quadrature format when the following conditions are met:
1) the ODE is of first order and the right hand sides below depend only on x or y(x):
quadrature_1_x_ode := diff(y(x),x)=F(x);
quadrature_1_y_ode := diff(y(x),x)=F(y(x));
2) the ODE is of high order and the right hand side depends only on x. For example:
quadrature_h_x_ode := diff(y(x),x,x,x,x)=F(x);
where F is an arbitrary function. These ODEs are just integrals in disguised format, and are solved mainly by integrating both sides.
From the point of view of their symmetries, all ODEs "missing y" have the symmetry [xi = 0, eta = 1], and all ODEs "missing x" have the symmetry [xi = 1, eta = 0] (see symgen);
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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