74.5.19 problem 19

Internal problem ID [15983]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.3, page 49
Problem number : 19
Date solved : Tuesday, January 28, 2025 at 08:25:37 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 14

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

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

✓ Solution by Mathematica

Time used: 0.026 (sec). Leaf size: 24

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

\begin{align*} y(x)\to -1+c_1 e^{\frac {x^2}{2}} \\ y(x)\to -1 \\ \end{align*}