Internal problem ID [5815]
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: 17.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (x^{2}+2\right ) y^{\prime \prime }+3 x y^{\prime }-y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 44
Order:=8; dsolve((x^2+2)*diff(y(x),x$2)+3*x*diff(y(x),x)-y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \left (1+\frac {1}{4} x^{2}-\frac {7}{96} x^{4}+\frac {161}{5760} x^{6}\right ) y \relax (0)+\left (x -\frac {1}{6} x^{3}+\frac {7}{120} x^{5}-\frac {17}{720} x^{7}\right ) D\relax (y )\relax (0)+O\left (x^{8}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 56
AsymptoticDSolveValue[(x^2+2)*y''[x]+3*x*y'[x]-y[x]==0,y[x],{x,0,7}]
\[ y(x)\to c_2 \left (-\frac {17 x^7}{720}+\frac {7 x^5}{120}-\frac {x^3}{6}+x\right )+c_1 \left (\frac {161 x^6}{5760}-\frac {7 x^4}{96}+\frac {x^2}{4}+1\right ) \]