46.1.2 problem 7

Internal problem ID [7292]
Book : ADVANCED ENGINEERING MATHEMATICS. ERWIN KREYSZIG, HERBERT KREYSZIG, EDWARD J. NORMINTON. 10th edition. John Wiley USA. 2011
Section : Chapter 5. Series Solutions of ODEs. Special Functions. Problem set 5.1. page 174
Problem number : 7
Date solved : Monday, January 27, 2025 at 02:49:48 PM
CAS classification : [_separable]

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

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 24

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

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

✓ Solution by Mathematica

Time used: 0.001 (sec). Leaf size: 20

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

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