76.5.26 problem 27

Internal problem ID [17446]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.7 (Substitution Methods). Problems at page 108
Problem number : 27
Date solved : Tuesday, January 28, 2025 at 10:37:54 AM
CAS classification : [_linear]

\begin{align*} x y^{\prime }+\left (1+x \right ) y&=x \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 17

dsolve(x*diff(y(x),x)+(x+1)*y(x)=x,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.056 (sec). Leaf size: 35

DSolve[x*D[y[x],x]+(x+1)*y[x]==x,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {e^{-x-1} \left (\int _1^xe^{K[1]+1} K[1]dK[1]+c_1\right )}{x} \]