39.6.4 problem Problem 27.37

Internal problem ID [6562]
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 27.37
Date solved : Monday, January 27, 2025 at 02:12:17 PM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

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

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 37

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

\[ y = \left (1+x^{2}+\frac {1}{2} x^{4}\right ) y \left (0\right )+\left (x +\frac {2}{3} x^{3}+\frac {4}{15} x^{5}\right ) y^{\prime }\left (0\right )+O\left (x^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.001 (sec). Leaf size: 38

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

\[ y(x)\to c_2 \left (\frac {4 x^5}{15}+\frac {2 x^3}{3}+x\right )+c_1 \left (\frac {x^4}{2}+x^2+1\right ) \]