50.8.20 problem 4(d)

Internal problem ID [7936]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 1. What is a differential equation. Problems for Review and Discovery. Page 53
Problem number : 4(d)
Date solved : Monday, January 27, 2025 at 03:33:16 PM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} x y^{\prime \prime }-3 y^{\prime }&=5 x \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 21

dsolve(x*diff(y(x),x$2)-3*diff(y(x),x)=5*x,y(x), singsol=all)
 

\[ y = \frac {\left (2 c_{1} x^{2}-5\right )^{2}}{16 c_{1}}+c_{2} \]

✓ Solution by Mathematica

Time used: 0.028 (sec). Leaf size: 24

DSolve[x*D[y[x],{x,2}]-3*D[y[x],x]==5*x,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {c_1 x^4}{4}-\frac {5 x^2}{4}+c_2 \]