Internal problem ID [10226]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter V, Singular solutions. Article 33. Page 73
Problem number: Ex 2.
ODE order: 1.
ODE degree: 3.
CAS Maple gives this as type [[_homogeneous, class C], _dAlembert]
Solve \begin {gather*} \boxed {8 \left (y^{\prime }+1\right )^{3}-27 \left (x +y\right ) \left (1-y^{\prime }\right )^{3}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.157 (sec). Leaf size: 132
dsolve(8*(1+diff(y(x),x))^3=27*(x+y(x))*(1-diff(y(x),x))^3,y(x), singsol=all)
\begin{align*} y \relax (x ) = -x \\ \frac {x}{2}-\frac {4 \ln \left (27 y \relax (x )+27 x +8\right )}{27}+\frac {4 \ln \left (9 \left (y \relax (x )+x \right )^{\frac {2}{3}}-6 \left (y \relax (x )+x \right )^{\frac {1}{3}}+4\right )}{27}+\frac {4 \ln \left (2+3 \left (y \relax (x )+x \right )^{\frac {1}{3}}\right )}{27}-\frac {y \relax (x )}{2}-\frac {\left (y \relax (x )+x \right )^{\frac {2}{3}}}{2}-c_{1} = 0 \\ \frac {x}{2}-\frac {y \relax (x )}{2}-\frac {\left (i \sqrt {3}-1\right ) \left (y \relax (x )+x \right )^{\frac {2}{3}}}{4}-c_{1} = 0 \\ \frac {x}{2}-\frac {y \relax (x )}{2}+\frac {\left (1+i \sqrt {3}\right ) \left (y \relax (x )+x \right )^{\frac {2}{3}}}{4}-c_{1} = 0 \\ \end{align*}
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[8*(1+y'[x])^3==27*(x+y[x])*(1-y'[x])^3,y[x],x,IncludeSingularSolutions -> True]
Timed out