Internal problem ID [5899]
Book: DIFFERENTIAL EQUATIONS with Boundary Value Problems. DENNIS G. ZILL,
WARREN S. WRIGHT, MICHAEL R. CULLEN. Brooks/Cole. Boston, MA. 2013. 8th
edition.
Section: CHAPTER 6 SERIES SOLUTIONS OF LINEAR EQUATIONS. CHAPTER 6 IN REVIEW.
Page 271
Problem number: 18.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+x y^{\prime }+y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = -6, y^{\prime }\relax (1) = 3] \end {align*}
With the expansion point for the power series method at \(x = 1\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 22
Order:=8; dsolve([diff(y(x),x$2)+x*diff(y(x),x)+y(x)=0,y(1) = -6, D(y)(1) = 3],y(x),type='series',x=1);
\[ y \relax (x ) = -6+3 \left (x -1\right )+\frac {3}{2} \left (x -1\right )^{2}-\frac {3}{2} \left (x -1\right )^{3}+\frac {3}{10} \left (x -1\right )^{5}-\frac {1}{20} \left (x -1\right )^{6}-\frac {1}{28} \left (x -1\right )^{7}+\mathrm {O}\left (\left (x -1\right )^{8}\right ) \]
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 55
AsymptoticDSolveValue[{y''[x]+x*y'[x]+y[x]==0,{y[1]==-6,y'[1]==3}},y[x],{x,1,7}]
\[ y(x)\to -\frac {1}{28} (x-1)^7-\frac {1}{20} (x-1)^6+\frac {3}{10} (x-1)^5-\frac {3}{2} (x-1)^3+\frac {3}{2} (x-1)^2+3 (x-1)-6 \]