7.15.28 problem 28

Internal problem ID [484]
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 : 28
Date solved : Monday, January 27, 2025 at 02:54:02 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x y^{\prime \prime }+2 y^{\prime }-4 y x&=0 \end{align*}

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 32

Order:=6; 
dsolve(x*diff(y(x),x$2)+2*diff(y(x),x)-4*x*y(x)=0,y(x),type='series',x=0);
 

\[ y = c_1 \left (1+\frac {2}{3} x^{2}+\frac {2}{15} x^{4}+\operatorname {O}\left (x^{6}\right )\right )+\frac {c_2 \left (1+2 x^{2}+\frac {2}{3} x^{4}+\operatorname {O}\left (x^{6}\right )\right )}{x} \]

✓ Solution by Mathematica

Time used: 0.009 (sec). Leaf size: 40

AsymptoticDSolveValue[x*D[y[x],{x,2}]+2*D[y[x],x]-4*x*y[x]==0,y[x],{x,0,"6"-1}]
 

\[ y(x)\to c_1 \left (\frac {2 x^3}{3}+2 x+\frac {1}{x}\right )+c_2 \left (\frac {2 x^4}{15}+\frac {2 x^2}{3}+1\right ) \]