Internal problem ID [5813]
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: 15.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-\left (1+x \right ) y^{\prime }-y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 74
Order:=8; dsolve(diff(y(x),x$2)-(x+1)*diff(y(x),x)-y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \left (1+\frac {1}{2} x^{2}+\frac {1}{6} x^{3}+\frac {1}{6} x^{4}+\frac {1}{15} x^{5}+\frac {7}{180} x^{6}+\frac {19}{1260} x^{7}\right ) y \relax (0)+\left (x +\frac {1}{2} x^{2}+\frac {1}{2} x^{3}+\frac {1}{4} x^{4}+\frac {3}{20} x^{5}+\frac {1}{15} x^{6}+\frac {13}{420} x^{7}\right ) D\relax (y )\relax (0)+O\left (x^{8}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 98
AsymptoticDSolveValue[y''[x]-(x+1)*y'[x]-y[x]==0,y[x],{x,0,7}]
\[ y(x)\to c_1 \left (\frac {19 x^7}{1260}+\frac {7 x^6}{180}+\frac {x^5}{15}+\frac {x^4}{6}+\frac {x^3}{6}+\frac {x^2}{2}+1\right )+c_2 \left (\frac {13 x^7}{420}+\frac {x^6}{15}+\frac {3 x^5}{20}+\frac {x^4}{4}+\frac {x^3}{2}+\frac {x^2}{2}+x\right ) \]