7.14.16 problem 16

Internal problem ID [441]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 3. Power series methods. Section 3.2 (Series solution near ordinary points). Problems at page 216
Problem number : 16
Date solved : Monday, January 27, 2025 at 02:53:40 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y&=0 \end{align*}

Using series method with expansion around

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

With initial conditions

\begin{align*} y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 5

Order:=6; 
dsolve([(1+x^2)*diff(y(x),x$2)+2*x*diff(y(x),x)-2*y(x)=0,y(0) = 0, D(y)(0) = 1],y(x),type='series',x=0);
 

\[ y = x \]

✓ Solution by Mathematica

Time used: 0.001 (sec). Leaf size: 4

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

\[ y(x)\to x \]