3.20 problem 15

Internal problem ID [12634]

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.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [[_homogeneous, `class C`], _dAlembert]

\[ \boxed {y^{\prime }-\ln \left (y+x \right )=0} \]

✓ Solution by Maple

Time used: 0.031 (sec). Leaf size: 29

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

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

✓ Solution by Mathematica

Time used: 0.207 (sec). Leaf size: 22

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

\[ \text {Solve}\left [\frac {\operatorname {ExpIntegralEi}(\log (x+y(x))+1)}{e}-x=c_1,y(x)\right ] \]