44.6.33 problem 33

Internal problem ID [7177]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 2. First order differential equations. Section 2.3 Linear equations. Exercises 2.3 at page 63
Problem number : 33
Date solved : Tuesday, February 04, 2025 at 12:44:27 AM
CAS classification : [_linear]

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

With initial conditions

\begin{align*} y \left (1\right )&=10 \end{align*}

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 19

dsolve([(x+1)*diff(y(x),x)+y(x)=ln(x),y(1) = 10],y(x), singsol=all)
 

\[ y = \frac {x \ln \left (x \right )-x +21}{x +1} \]

✓ Solution by Mathematica

Time used: 0.032 (sec). Leaf size: 20

DSolve[{(x+1)*D[y[x],x]+y[x]==Log[x],{y[1]==10}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {-x+x \log (x)+21}{x+1} \]