74.7.46 problem 46

Internal problem ID [16123]
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
Date solved : Tuesday, January 28, 2025 at 08:50:11 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 15

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

\[ y = c_{1} x^{2} {\mathrm e}^{-\frac {x^{3}}{3}} \]

✓ Solution by Mathematica

Time used: 0.050 (sec). Leaf size: 35

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

\begin{align*} y(x)\to c_1 \exp \left (\int _1^x\frac {2-K[1]^3}{K[1]}dK[1]\right ) \\ y(x)\to 0 \\ \end{align*}