Learning Guide Learning Guide

232 • Chapter 6: Examples from CalculusThe dsolve CommandThe most commonly used command for investigating the behavior of ordinarydifferential equations (ODEs) in Maple is dsolve. You can use thisgeneral-purpose tool to obtain both closed form and numerical solutionsto a wide variety of ODEs. This is the basic syntax of dsolve.dsolve(eqns, vars)Here eqns is a set of differential equations and initial values, and vars isa set of variables with respect to which dsolve solves.The following example is a differential equation and an initial condition.> eq := diff(v(t),t)+2*t = 0;eq := ( d dt v(t)) + 2 t = 0> ini := v(1) = 5;ini := v(1) = 5Use dsolve to obtain the solution.> dsolve( {eq, ini}, {v(t)} );v(t) = −t 2 + 6If you omit some or all of the initial conditions, then dsolve returnsa solution containing arbitrary constants of the form _Cnumber.> eq := diff(y(x),x$2) - y(x) = 1;eq := ( d2y(x)) − y(x) = 1dx2 > dsolve( {eq}, {y(x)} );