4.4 problem 4

Internal problem ID [4491]

Book: Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section: Chapter 2, First order differential equations. Review problems. page 79
Problem number: 4.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_linear]

Solve \begin {gather*} \boxed {y^{\prime }+\frac {3 y}{x}-x^{2}+4 x -3=0} \end {gather*}

Solution by Maple

Time used: 0.002 (sec). Leaf size: 23

dsolve(diff(y(x),x)+3*y(x)/x=x^2-4*x+3,y(x), singsol=all)
 

\[ y \relax (x ) = \frac {x^{3}}{6}-\frac {4 x^{2}}{5}+\frac {3 x}{4}+\frac {c_{1}}{x^{3}} \]

Solution by Mathematica

Time used: 0.031 (sec). Leaf size: 31

DSolve[y'[x]+3*y[x]/x==x^2-4*x+3,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {x^3}{6}+\frac {c_1}{x^3}-\frac {4 x^2}{5}+\frac {3 x}{4} \\ \end{align*}