Internal problem ID [4386]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-3 y x^{2}=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.001 (sec). Leaf size: 14
Order:=6; dsolve(diff(y(x),x)=3*x^2*y(x),y(x),type='series',x=0);
\[ y \relax (x ) = \left (x^{3}+1\right ) y \relax (0)+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 11
AsymptoticDSolveValue[y'[x]==3*x^2*y[x],y[x],{x,0,5}]
\[ y(x)\to c_1 \left (x^3+1\right ) \]