Learning Guide Learning Guide

6.2 Ordinary Differential Equations • 241{x 2 (t) = 50121( 1110 t2 + 910 − 11 5 t + 1 5 cosh( 110Heaviside(t − 1) + 2 11 − 2 11 cosh( 1= − 1001Heaviside(t − 1) cosh(121 10√ −11√100 (t − 1)))√ √−11 100 t), x1 (t)10√ √−11 100 (t − 1))− 2 11 cosh( 1 10√ −11√100 t) + e (−1/10 √ −11 √ 100 t)+ e (1/10 √ −11 √ 100 t) 5 + Heaviside(t − 1) t211− 1011 Heaviside(t − 1) t + 2 11 + 155 Heaviside(t − 1)}121As expected, you get the same solution as before.The type=series Option The series method for solving differentialequations finds an approximate symbolic solution to the equations inthe following manner. Maple finds a series approximation to the equations.It then solves the series approximation symbolically, using exactmethods. This technique is useful when Maple’s standard algorithms fail,but you still want a symbolic solution rather than a purely numeric solution.The series method can often help with nonlinear and high-orderODEs.When using the series method, Maple assumes that a solution of theform( ∞)∑x c a i x ii=0exists, where c is a rational number.Consider the following differential equation.> eq := 2*x*diff(y(x),x,x) + diff(y(x),x) + y(x) = 0;eq := 2 x ( d2dx 2 y(x)) + ( d y(x)) + y(x) = 0dxSolve the equation.> dsolve( {eq}, {y(x)}, type=series );