7.15.18 problem 18

Internal problem ID [474]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 3. Power series methods. Section 3.3 (Regular singular points). Problems at page 231
Problem number : 18
Date solved : Monday, January 27, 2025 at 02:53:59 AM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} 2 x y^{\prime \prime }+3 y^{\prime }-y&=0 \end{align*}

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 44

Order:=6; 
dsolve(2*x*diff(y(x),x$2)+3*diff(y(x),x)-y(x)=0,y(x),type='series',x=0);
 

\[ y = \frac {c_1 \left (1+x +\frac {1}{6} x^{2}+\frac {1}{90} x^{3}+\frac {1}{2520} x^{4}+\frac {1}{113400} x^{5}+\operatorname {O}\left (x^{6}\right )\right )}{\sqrt {x}}+c_2 \left (1+\frac {1}{3} x +\frac {1}{30} x^{2}+\frac {1}{630} x^{3}+\frac {1}{22680} x^{4}+\frac {1}{1247400} x^{5}+\operatorname {O}\left (x^{6}\right )\right ) \]

✓ Solution by Mathematica

Time used: 0.002 (sec). Leaf size: 81

AsymptoticDSolveValue[2*x*D[y[x],{x,2}]+3*D[y[x],x]-y[x]==0,y[x],{x,0,"6"-1}]
 

\[ y(x)\to c_1 \left (\frac {x^5}{1247400}+\frac {x^4}{22680}+\frac {x^3}{630}+\frac {x^2}{30}+\frac {x}{3}+1\right )+\frac {c_2 \left (\frac {x^5}{113400}+\frac {x^4}{2520}+\frac {x^3}{90}+\frac {x^2}{6}+x+1\right )}{\sqrt {x}} \]