Internal problem ID [14389]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 2. First Order Equations. Exercises 2.5, page 64
Problem number: 46.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }-\frac {2 y}{x}+x^{2} y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 15
dsolve(diff(y(x),x)-(2/x)*y(x)=-x^2*y(x),y(x), singsol=all)
\[ y \left (x \right ) = c_{1} x^{2} {\mathrm e}^{-\frac {x^{3}}{3}} \]
✓ Solution by Mathematica
Time used: 0.033 (sec). Leaf size: 25
DSolve[y'[x]-(2/x)*y[x]==-x^2*y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 e^{-\frac {x^3}{3}} x^2 \\ y(x)\to 0 \\ \end{align*}