43.2.4 problem 7.3.6

Internal problem ID [6861]
Book : Notes on Diffy Qs. Differential Equations for Engineers. By by Jiri Lebl, 2013.
Section : Chapter 7. POWER SERIES METHODS. 7.3.2 The method of Frobenius. Exercises. page 300
Problem number : 7.3.6
Date solved : Monday, January 27, 2025 at 02:31:51 PM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} 2 x y^{\prime \prime }+y^{\prime }-x^{2} 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: 28

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

\[ y = c_1 \sqrt {x}\, \left (1+\frac {1}{21} x^{3}+\operatorname {O}\left (x^{6}\right )\right )+c_2 \left (1+\frac {1}{15} x^{3}+\operatorname {O}\left (x^{6}\right )\right ) \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 33

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

\[ y(x)\to c_1 \sqrt {x} \left (\frac {x^3}{21}+1\right )+c_2 \left (\frac {x^3}{15}+1\right ) \]