28.1.120 problem 143

Internal problem ID [4426]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page 78
Problem number : 143
Date solved : Monday, January 27, 2025 at 09:16:55 AM
CAS classification : [[_2nd_order, _missing_y]]

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

✓ Solution by Maple

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

dsolve(x*diff(y(x),x$2)=diff(y(x),x)+x,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {\ln \left (x \right ) x^{2}}{2}+\frac {\left (2 c_{1} -1\right ) x^{2}}{4}+c_{2} \]

✓ Solution by Mathematica

Time used: 0.028 (sec). Leaf size: 30

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

\[ y(x)\to \frac {1}{2} x^2 \log (x)+\frac {1}{4} (-1+2 c_1) x^2+c_2 \]