SolveODE Command

SolveODE[ <f'(x,y)>, <Start x>, <Start y>, <End x>, <Step> ]

Solves first order ordinary differential equations (ODE) \frac{dy}{dx}=f'(x,y) numerically given start point and end & step for x.

For example to solve \frac{dy}{dx}=-xy using A as a starting point, enter SolveODE[-x*y, x(A), y(A), 5, 0.1]

Note: Length[ <Locus> ] allows you to find out how many points are in the computed locus and First[ <Locus>, <Number> ] allows you to extract the points as a list, for example First[loc1, Length[loc1]].

Note: To find the "reverse" solution, just enter a negative value for End x, eg SolveODE[-x*y, x(A), y(A), -5, 0.1]

SolveODE[ <f(x,y)>, <g(x,y)>, <Start x>, <Start y>, <End t>, <Step> ]

Solves first order ODE \frac{dy}{dx}=\frac{f(x,y)}{g(x,y)} given start point, maximal value of an internal parameter t and step for t. This version of the command may work where the first one fails eg when the solution curve has vertical points.

For example, to solve \frac{dy}{dx}=- \frac{x}{y} using A as a starting point, enter SolveODE[-x, y, x(A), y(A), 5, 0.1].

Note: To find the "reverse" solution, just enter a negative value for End t, eg SolveODE[-x, y, x(A), y(A), -5, 0.1]

SolveODE[ <b(x)>, <c(x)>, <f(x)>, <Start x>, <Start y>, <Start y'>, <End x>, <Step>]

Solves second order ODE y''+b(x)y'+c(x)y=f(x).

Note: Always returns the result as locus. The algorithms are currently based on Runge-Kutta numeric methods.

CAS Syntax

Following two syntaxes work only in CAS View.

SolveODE[ <f(x, y)> ]

Attempts to find the exact solution of the first order ODE \frac{dy}{dx}(x)=f(x, y(x)).

Example:

SolveODE[y / x] yields y = c₁ x.

SolveODE[ <f(v, w)>, <Dependent Variable v>, <Independent Variable w> ]

Attempts to find the exact solution of the first order ODE \frac{dv}{dw}(w)=f(w, v(w)).

Example:

SolveODE[y / x, y, x] yields y = c₁ x.