75.11.8 problem 267

Internal problem ID [16859]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 11. Singular solutions of differential equations. Exercises page 92
Problem number : 267
Date solved : Tuesday, January 28, 2025 at 09:35:33 AM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

\begin{align*} 8 {y^{\prime }}^{3}-12 {y^{\prime }}^{2}&=27 y-27 x \end{align*}

✓ Solution by Maple

Time used: 0.082 (sec). Leaf size: 37

dsolve(8*diff(y(x),x)^3-12*diff(y(x),x)^2=27*(y(x)-x),y(x), singsol=all)
 

\begin{align*} y &= x -\frac {4}{27} \\ y &= \left (-x +c_{1} \right ) \sqrt {x -c_{1}}+c_{1} \\ y &= \left (x -c_{1} \right )^{{3}/{2}}+c_{1} \\ \end{align*}

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[8*D[y[x],x]^3-12*D[y[x],x]^2==27*(y[x]-x),y[x],x,IncludeSingularSolutions -> True]
 

Timed out