Internal problem ID [5846]
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. 6.3 SOLUTIONS ABOUT
SINGULAR POINTS. EXERCISES 6.3. Page 255
Problem number: 16.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {2 x y^{\prime \prime }+5 y^{\prime }+y x=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 36
Order:=8; dsolve(2*x*diff(y(x),x$2)+5*diff(y(x),x)+x*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \frac {c_{2} \left (1-\frac {1}{14} x^{2}+\frac {1}{616} x^{4}-\frac {1}{55440} x^{6}+\mathrm {O}\left (x^{8}\right )\right ) x^{\frac {3}{2}}+c_{1} \left (1-\frac {1}{2} x^{2}+\frac {1}{40} x^{4}-\frac {1}{2160} x^{6}+\mathrm {O}\left (x^{8}\right )\right )}{x^{\frac {3}{2}}} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 61
AsymptoticDSolveValue[2*x*y''[x]+5*y'[x]+x*y[x]==0,y[x],{x,0,7}]
\[ y(x)\to c_1 \left (-\frac {x^6}{55440}+\frac {x^4}{616}-\frac {x^2}{14}+1\right )+\frac {c_2 \left (-\frac {x^6}{2160}+\frac {x^4}{40}-\frac {x^2}{2}+1\right )}{x^{3/2}} \]