74.5.18 problem 18

Internal problem ID [15982]
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 : 18
Date solved : Tuesday, January 28, 2025 at 08:25:35 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }+y x&=x^{3} \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 17

dsolve(diff(y(x),x)+y(x)*x=x^3,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.068 (sec). Leaf size: 22

DSolve[D[y[x],x]+y[x]*x==x^3,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x^2+c_1 e^{-\frac {x^2}{2}}-2 \]