58.1.18 problem 18

Internal problem ID [9089]
Book : Second order enumerated odes
Section : section 1
Problem number : 18
Date solved : Monday, January 27, 2025 at 05:37:13 PM
CAS classification : [[_2nd_order, _missing_y]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 21

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

\[ y = \frac {x^{2}}{2}-c_{1} {\mathrm e}^{-x}-x +c_{2} \]

✓ Solution by Mathematica

Time used: 0.043 (sec). Leaf size: 27

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

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