58.2.43 problem 43

Internal problem ID [9166]
Book : Second order enumerated odes
Section : section 2
Problem number : 43
Date solved : Monday, January 27, 2025 at 05:51:33 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }-x \left (6+x \right ) y^{\prime }+10 y&=0 \end{align*}

Using series method with expansion around

\begin{align*} 0 \end{align*}

✓ Solution by Maple

Time used: 0.017 (sec). Leaf size: 62

Order:=6; 
dsolve(x^2*diff(y(x),x$2)-x*(x+6)*diff(y(x),x)+10*y(x)=0,y(x),type='series',x=0);
 

\[ y = x^{2} \left (c_{1} x^{3} \left (1+\frac {5}{4} x +\frac {3}{4} x^{2}+\frac {7}{24} x^{3}+\frac {1}{12} x^{4}+\frac {3}{160} x^{5}+\operatorname {O}\left (x^{6}\right )\right )+c_{2} \left (\ln \left (x \right ) \left (24 x^{3}+30 x^{4}+18 x^{5}+\operatorname {O}\left (x^{6}\right )\right )+\left (12-12 x +18 x^{2}+26 x^{3}+x^{4}-9 x^{5}+\operatorname {O}\left (x^{6}\right )\right )\right )\right ) \]

✓ Solution by Mathematica

Time used: 0.030 (sec). Leaf size: 84

AsymptoticDSolveValue[x^2*D[y[x],{x,2}]-x*(x+6)*D[y[x],x]+10*y[x]==0,y[x],{x,0,"6"-1}]
 

\[ y(x)\to c_1 \left (\frac {1}{2} x^5 (5 x+4) \log (x)-\frac {1}{4} x^2 \left (3 x^4-6 x^3-6 x^2+4 x-4\right )\right )+c_2 \left (\frac {x^9}{12}+\frac {7 x^8}{24}+\frac {3 x^7}{4}+\frac {5 x^6}{4}+x^5\right ) \]