Internal problem ID [2512]
Book: Mathematical methods for physics and engineering, Riley, Hobson, Bence, second edition,
2002
Section: Chapter 14, First order ordinary differential equations. 14.4 Exercises, page
490
Problem number: Problem 14.31.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]]
\[ \boxed {y^{\prime \prime }+{y^{\prime }}^{2}+y^{\prime }=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 18
dsolve([diff(y(x),x$2)+ (diff(y(x),x))^2+diff(y(x),x)=0,y(0) = 0],y(x), singsol=all)
\[ y \left (x \right ) = \ln \left (c_{2} {\mathrm e}^{x}-c_{2} +1\right )-x \]
✓ Solution by Mathematica
Time used: 0.395 (sec). Leaf size: 54
DSolve[{y''[x]+(y'[x])^2+y'[x]==0,y[0]==0},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \log \left (-e^x\right )-\log \left (e^x\right )-i \pi \\ y(x)\to -\log \left (e^x\right )+\log \left (-e^x+e^{c_1}\right )-\log \left (-1+e^{c_1}\right ) \\ \end{align*}