Internal problem ID [4387]
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 elementary method.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-3 x^{2} y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 10
dsolve(diff(y(x),x)=3*x^2*y(x),y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{x^{3}} \]
✓ Solution by Mathematica
Time used: 0.036 (sec). Leaf size: 18
DSolve[y'[x]==3*x^2*y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 e^{x^3} \\ y(x)\to 0 \\ \end{align*}