Internal problem ID [5825]
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. Section 6.2 SOLUTIONS
ABOUT ORDINARY POINTS. EXERCISES 6.2. Page 246
Problem number: 26 (a).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-y x -1=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 38
Order:=8; dsolve(diff(y(x),x$2)-x*y(x)=1,y(x),type='series',x=0);
\[ y \relax (x ) = \left (1+\frac {1}{6} x^{3}+\frac {1}{180} x^{6}\right ) y \relax (0)+\left (x +\frac {1}{12} x^{4}+\frac {1}{504} x^{7}\right ) D\relax (y )\relax (0)+\frac {x^{2}}{2}+\frac {x^{5}}{40}+O\left (x^{8}\right ) \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 56
AsymptoticDSolveValue[y''[x]-x*y[x]==1,y[x],{x,0,7}]
\[ y(x)\to \frac {x^5}{40}+\frac {x^2}{2}+c_2 \left (\frac {x^7}{504}+\frac {x^4}{12}+x\right )+c_1 \left (\frac {x^6}{180}+\frac {x^3}{6}+1\right ) \]