Internal problem ID [2281]
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: 9.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y^{\prime \prime }-{y^{\prime }}^{3}-y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 73
dsolve(diff(y(x),x$2)=diff(y(x),x)^3+diff(y(x),x),y(x), singsol=all)
\begin{align*} y \left (x \right ) &= -\frac {\arctan \left (\frac {2 c_{1} {\mathrm e}^{2 x}-1}{2 \sqrt {-\left (c_{1} {\mathrm e}^{2 x}-1\right ) {\mathrm e}^{2 x} c_{1}}}\right )}{2}+c_{2} \\ y \left (x \right ) &= \frac {\arctan \left (\frac {2 c_{1} {\mathrm e}^{2 x}-1}{2 \sqrt {-\left (c_{1} {\mathrm e}^{2 x}-1\right ) {\mathrm e}^{2 x} c_{1}}}\right )}{2}+c_{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 60.102 (sec). Leaf size: 71
DSolve[y''[x]==y'[x]^3+y'[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_2-i \log \left (\sqrt {-1+e^{2 (x+c_1)}}-e^{x+c_1}\right ) \\ y(x)\to i \log \left (\sqrt {-1+e^{2 (x+c_1)}}-e^{x+c_1}\right )+c_2 \\ \end{align*}