71.3.20 problem 15

Internal problem ID [14370]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 2. The Initial Value Problem. Exercises 2.1, page 40
Problem number : 15
Date solved : Tuesday, January 28, 2025 at 06:27:56 AM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

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

✓ Solution by Maple

Time used: 0.066 (sec). Leaf size: 29

dsolve(diff(y(x),x)=ln(x+y(x)),y(x), singsol=all)
 

\[ y = {\mathrm e}^{\operatorname {RootOf}\left (c_{1} {\mathrm e}-x \,{\mathrm e}-\operatorname {Ei}_{1}\left (-\textit {\_Z} -1\right )\right )}-x \]

✓ Solution by Mathematica

Time used: 0.198 (sec). Leaf size: 161

DSolve[D[y[x],x]==Log[x+y[x]],y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\int _1^x-\frac {\log (K[1]+y(x))}{\log (K[1]+y(x))+1}dK[1]+\int _1^{y(x)}-\frac {\log (x+K[2]) \int _1^x\left (\frac {\log (K[1]+K[2])}{(K[1]+K[2]) (\log (K[1]+K[2])+1)^2}-\frac {1}{(K[1]+K[2]) (\log (K[1]+K[2])+1)}\right )dK[1]+\int _1^x\left (\frac {\log (K[1]+K[2])}{(K[1]+K[2]) (\log (K[1]+K[2])+1)^2}-\frac {1}{(K[1]+K[2]) (\log (K[1]+K[2])+1)}\right )dK[1]-1}{\log (x+K[2])+1}dK[2]=c_1,y(x)\right ] \]