Internal problem ID [2003]
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]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+\left (y^{\prime }\right )^{2}+y^{\prime }=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.078 (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)
\[ y \relax (x ) = \ln \left (1+\left ({\mathrm e}^{x}-1\right ) c_{2}\right )-x \]
✓ Solution by Mathematica
Time used: 0.376 (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*}