35.9.3 problem 2, using series method

Internal problem ID [6238]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 12, Series Solutions of Differential Equations. Section 1. Miscellaneous problems. page 564
Problem number : 2, using series method
Date solved : Monday, January 27, 2025 at 01:49:47 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=3 x^{2} y \end{align*}

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 17

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

\[ y = \left (x^{3}+1\right ) y \left (0\right )+O\left (x^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.001 (sec). Leaf size: 11

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

\[ y(x)\to c_1 \left (x^3+1\right ) \]