Maple Professional
Maple Academic
Maple Student Edition
Maple Personal Edition
Maple Player
Maple Player for iPad
MapleSim Professional
MapleSim Academic
Maple T.A. - Testing & Assessment
Maple T.A. MAA Placement Test Suite
Möbius - Online Courseware
Machine Design / Industrial Automation
Aerospace
Vehicle Engineering
Robotics
Power Industries
System Simulation and Analysis
Model development for HIL
Plant Modeling for Control Design
Robotics/Motion Control/Mechatronics
Other Application Areas
Mathematics Education
Engineering Education
High Schools & Two-Year Colleges
Testing & Assessment
Students
Financial Modeling
Operations Research
High Performance Computing
Physics
Live Webinars
Recorded Webinars
Upcoming Events
MaplePrimes
Maplesoft Blog
Maplesoft Membership
Maple Ambassador Program
MapleCloud
Technical Whitepapers
E-Mail Newsletters
Maple Books
Math Matters
Application Center
MapleSim Model Gallery
User Case Studies
Exploring Engineering Fundamentals
Teaching Concepts with Maple
Maplesoft Welcome Center
Teacher Resource Center
Student Help Center
Solving ODEs That Are in Quadrature Format
Description
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.
Examples
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, 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.
Download Help Document
