36.4.4 problem 4

Internal problem ID [6342]
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
Date solved : Monday, January 27, 2025 at 01:57:38 PM
CAS classification : [_linear]

\begin{align*} y^{\prime }+\frac {3 y}{x}&=x^{2}-4 x +3 \end{align*}

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 23

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

\[ y = \frac {x^{3}}{6}-\frac {4 x^{2}}{5}+\frac {3 x}{4}+\frac {c_1}{x^{3}} \]

✓ Solution by Mathematica

Time used: 0.048 (sec). Leaf size: 31

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

\[ y(x)\to \frac {x^3}{6}+\frac {c_1}{x^3}-\frac {4 x^2}{5}+\frac {3 x}{4} \]