Maple 9 Learning Guide - Maplesoft

260 • Chapter 7: Solving Calculus Problems_Y(0) + D(_Y )(0) x − 17 6 _Y(0) x2 +(− 1723D(_Y )(0) +18 18 _Y(0)) x3 +( 289 23_Y(0) +216 36 D(_Y )(0)) x4 +( 289833D(_Y )(0) −1080 540 _Y(0)) x5 + O(x 6 )The diff and int commands can also operate on DESol.Plotting Ordinary Differential EquationsYou cannot solve many differential equations analytically. In such cases,plotting the differential equation is advantageous.> ode1 :=> diff(y(t), t$2) + sin(t)^2*diff(y(t),t) + y(t) = cos(t)^2;ode1 := ( d2dt 2 y(t)) + sin(t)2 ( d y(t)) + y(t) = cos(t)2dt> ic1 := y(0) = 1, D(y)(0) = 0;ic1 := y(0) = 1, D(y)(0) = 0First, attempt to solve this ODE analytically by using dsolve.> dsolve({ode1, ic1}, {y(t)} );The dsolve command returned nothing, indicating that it could notfind a solution. Try Laplace methods.> dsolve( {ode1, ic1}, {y(t)}, method=laplace );Again, dsolve did not find a solution. Since dsolve was not successful,try the DEplot command found in the DEtools package.> with(DEtools):DEplot is a general ODE plotter which you can use with the followingsyntax.