Internal problem ID [6644]
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: 10.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]
\[ \boxed {y^{\prime \prime }-y^{\prime } x -y=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 44
Order:=8; dsolve(diff(y(x),x$2)-x*diff(y(x),x)-y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = \left (1+\frac {1}{2} x^{2}+\frac {1}{8} x^{4}+\frac {1}{48} x^{6}\right ) y \left (0\right )+\left (x +\frac {1}{3} x^{3}+\frac {1}{15} x^{5}+\frac {1}{105} x^{7}\right ) D\left (y \right )\left (0\right )+O\left (x^{8}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 56
AsymptoticDSolveValue[y''[x]-x*y'[x]-y[x]==0,y[x],{x,0,7}]
\[ y(x)\to c_2 \left (\frac {x^7}{105}+\frac {x^5}{15}+\frac {x^3}{3}+x\right )+c_1 \left (\frac {x^6}{48}+\frac {x^4}{8}+\frac {x^2}{2}+1\right ) \]