Internal problem ID [10792]
Book: Differential equations and the calculus of variations by L. ElSGOLTS. MIR PUBLISHERS,
MOSCOW, Third printing 1977.
Section: Chapter 1, First-Order Differential Equations. Problems page 88
Problem number: Problem 42.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _dAlembert]
\[ \boxed {y^{\prime }-\left (x -5 y\right )^{\frac {1}{3}}-2=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 80
dsolve(diff(y(x),x)=(x-5*y(x))^(1/3)+2,y(x), singsol=all)
\[ x +\frac {81 \ln \left (729+125 x -625 y \left (x \right )\right )}{125}-\frac {27 \left (x -5 y \left (x \right )\right )^{\frac {1}{3}}}{25}+\frac {162 \ln \left (5 \left (x -5 y \left (x \right )\right )^{\frac {1}{3}}+9\right )}{125}-\frac {81 \ln \left (25 \left (x -5 y \left (x \right )\right )^{\frac {2}{3}}-45 \left (x -5 y \left (x \right )\right )^{\frac {1}{3}}+81\right )}{125}+\frac {3 \left (x -5 y \left (x \right )\right )^{\frac {2}{3}}}{10}-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.218 (sec). Leaf size: 70
DSolve[y'[x]==(x-5*y[x])^(1/3)+2,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [5 y(x)+5 \left (-y(x)+\frac {3}{50} (x-5 y(x))^{2/3}-\frac {27}{125} \sqrt [3]{x-5 y(x)}+\frac {243}{625} \log \left (5 \sqrt [3]{x-5 y(x)}+9\right )+\frac {x}{5}\right )=c_1,y(x)\right ] \]