36.2.20 problem 20

Internal problem ID [6313]
Book : Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section : Chapter 2, First order differential equations. Section 2.3, Linear equations. Exercises. page 54
Problem number : 20
Date solved : Monday, January 27, 2025 at 01:55:53 PM
CAS classification : [_linear]

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

With initial conditions

\begin{align*} y \left (1\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 18

dsolve([diff(y(x),x)+3*y(x)/x+2=3*x,y(1) = 1],y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {3 x^{2}}{5}-\frac {x}{2}+\frac {9}{10 x^{3}} \]

✓ Solution by Mathematica

Time used: 0.032 (sec). Leaf size: 24

DSolve[{D[y[x],x]+3*y[x]/x+2==3*x,{y[1]==1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {6 x^5-5 x^4+9}{10 x^3} \]