Internal problem ID [5181]
Book: An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY
1961
Section: Chapter 1. Introduction– Linear equations of First Order. Page 45
Problem number: 1(b).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {x y^{\prime }+y-3 x^{3}+1=0} \end {gather*}
✓ Solution by Maple
Time used: 0.001 (sec). Leaf size: 18
dsolve(x*diff(y(x),x)+y(x)=3*x^3-1,y(x), singsol=all)
\[ y \relax (x ) = \frac {\frac {3}{4} x^{4}-x +c_{1}}{x} \]
✓ Solution by Mathematica
Time used: 0.029 (sec). Leaf size: 20
DSolve[x*y'[x]+y[x]==3*x^3-1,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {3 x^3}{4}+\frac {c_1}{x}-1 \\ \end{align*}