20.3.4 problem Problem 4

Internal problem ID [3613]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 1, First-Order Differential Equations. Section 1.6, First-Order Linear Differential Equations. page 59
Problem number : Problem 4
Date solved : Monday, January 27, 2025 at 07:47:37 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }+2 y x&=2 x^{3} \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 17

dsolve(diff(y(x),x)+2*x*y(x)=2*x^3,y(x), singsol=all)
 

\[ y \left (x \right ) = x^{2}-1+c_{1} {\mathrm e}^{-x^{2}} \]

✓ Solution by Mathematica

Time used: 0.031 (sec). Leaf size: 20

DSolve[D[y[x],x]+2*x*y[x]==2*x^3,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x^2+c_1 e^{-x^2}-1 \]