Internal problem ID [5812]
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: 14.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (2+x \right ) y^{\prime \prime }+x y^{\prime }-y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 39
Order:=8; dsolve((x+2)*diff(y(x),x$2)+x*diff(y(x),x)-y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \left (1+\frac {1}{4} x^{2}-\frac {1}{24} x^{3}+\frac {1}{480} x^{5}-\frac {1}{1440} x^{6}+\frac {1}{6720} x^{7}\right ) y \relax (0)+D\relax (y )\relax (0) x +O\left (x^{8}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 91
AsymptoticDSolveValue[(x+2)*y''[x]+x*y'[x]+y[x]==0,y[x],{x,0,7}]
\[ y(x)\to c_2 \left (\frac {29 x^7}{20160}-\frac {7 x^6}{1440}+\frac {x^5}{240}+\frac {x^4}{24}-\frac {x^3}{6}+x\right )+c_1 \left (\frac {x^7}{8064}+\frac {x^6}{576}-\frac {x^5}{96}+\frac {x^4}{48}+\frac {x^3}{24}-\frac {x^2}{4}+1\right ) \]