Internal problem ID [14943]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 1. Basic concepts and definitions. Exercises page 18
Problem number: 11.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _dAlembert]
\[ \boxed {y^{\prime }-\left (3 x -y\right )^{\frac {1}{3}}=-1} \]
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 86
dsolve(diff(y(x),x)=(3*x-y(x))^(1/3)-1,y(x), singsol=all)
\[ x +\frac {3 \left (3 x -y \left (x \right )\right )^{\frac {2}{3}}}{2}+32 \ln \left (-4+\left (3 x -y \left (x \right )\right )^{\frac {1}{3}}\right )-16 \ln \left (\left (3 x -y \left (x \right )\right )^{\frac {2}{3}}+4 \left (3 x -y \left (x \right )\right )^{\frac {1}{3}}+16\right )+16 \ln \left (-64+3 x -y \left (x \right )\right )+12 \left (3 x -y \left (x \right )\right )^{\frac {1}{3}}-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.203 (sec). Leaf size: 55
DSolve[y'[x]==(3*x-y[x])^(1/3)-1,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {3}{2} (3 x-y(x))^{2/3}+12 \sqrt [3]{3 x-y(x)}+48 \log \left (\sqrt [3]{3 x-y(x)}-4\right )+x=c_1,y(x)\right ] \]