7.15.22 problem 22

Internal problem ID [478]
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 : 22
Date solved : Monday, January 27, 2025 at 02:54:01 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 36

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

\[ y = \frac {c_2 \,x^{{5}/{2}} \left (1-\frac {1}{9} x^{2}+\frac {1}{234} x^{4}+\operatorname {O}\left (x^{6}\right )\right )+c_1 \left (1+x^{2}-\frac {1}{6} x^{4}+\operatorname {O}\left (x^{6}\right )\right )}{x} \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 46

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

\[ y(x)\to \frac {c_2 \left (-\frac {x^4}{6}+x^2+1\right )}{x}+c_1 \left (\frac {x^4}{234}-\frac {x^2}{9}+1\right ) x^{3/2} \]