39.6.1 problem Problem 27.28

Internal problem ID [6559]
Book : Schaums Outline Differential Equations, 4th edition. Bronson and Costa. McGraw Hill 2014
Section : Chapter 27. Power series solutions of linear DE with variable coefficients. Supplementary Problems. page 274
Problem number : Problem 27.28
Date solved : Monday, January 27, 2025 at 02:12:15 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (1+x \right ) y^{\prime \prime }+\frac {y^{\prime }}{x}+y x&=0 \end{align*}

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 38

Order:=6; 
dsolve((x+1)*diff(y(x),x$2)+1/x*diff(y(x),x)+x*y(x)=0,y(x),type='series',x=0);
 

\[ y = \left (c_2 \ln \left (x \right )+c_1 \right ) \left (1-\frac {1}{9} x^{3}+\frac {1}{24} x^{4}-\frac {1}{50} x^{5}+\operatorname {O}\left (x^{6}\right )\right )+\left (x +\frac {2}{27} x^{3}-\frac {11}{144} x^{4}+\frac {33}{1000} x^{5}+\operatorname {O}\left (x^{6}\right )\right ) c_2 \]

✓ Solution by Mathematica

Time used: 0.007 (sec). Leaf size: 82

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

\[ y(x)\to c_1 \left (-\frac {x^5}{50}+\frac {x^4}{24}-\frac {x^3}{9}+1\right )+c_2 \left (\frac {33 x^5}{1000}-\frac {11 x^4}{144}+\frac {2 x^3}{27}+\left (-\frac {x^5}{50}+\frac {x^4}{24}-\frac {x^3}{9}+1\right ) \log (x)+x\right ) \]