49.21.1 problem 1(a)

Internal problem ID [7731]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 5. Existence and uniqueness of solutions to first order equations. Page 190
Problem number : 1(a)
Date solved : Monday, January 27, 2025 at 03:10:51 PM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 12

dsolve(diff(y(x),x)=x^2*y(x),y(x), singsol=all)
 

\[ y = c_{1} {\mathrm e}^{\frac {x^{3}}{3}} \]

✓ Solution by Mathematica

Time used: 0.025 (sec). Leaf size: 22

DSolve[D[y[x],x]==x^2*y[x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to c_1 e^{\frac {x^3}{3}} \\ y(x)\to 0 \\ \end{align*}