15.18.16 problem 16

Internal problem ID [3259]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 35, page 157
Problem number : 16
Date solved : Monday, January 27, 2025 at 07:29:38 AM
CAS classification : [[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]]

\begin{align*} y^{\prime \prime }&={y^{\prime }}^{2}+y^{\prime } \end{align*}

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 16

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

\[ y \left (x \right ) = -\ln \left (-{\mathrm e}^{x} c_{1} -c_{2} \right ) \]

✓ Solution by Mathematica

Time used: 1.869 (sec). Leaf size: 31

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

\begin{align*} y(x)\to c_2-\log \left (-1+e^{x+c_1}\right ) \\ y(x)\to c_2-i \pi \\ \end{align*}