75.1.10 problem 11

Internal problem ID [16673]
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
Date solved : Tuesday, January 28, 2025 at 09:17:39 AM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

\begin{align*} y^{\prime }&=\left (3 x -y\right )^{{1}/{3}}-1 \end{align*}

✓ Solution by Maple

Time used: 0.066 (sec). Leaf size: 86

dsolve(diff(y(x),x)=(3*x-y(x))^(1/3)-1,y(x), singsol=all)
 

\[ x +\frac {3 \left (-y+3 x \right )^{{2}/{3}}}{2}+32 \ln \left (-4+\left (-y+3 x \right )^{{1}/{3}}\right )-16 \ln \left (\left (-y+3 x \right )^{{2}/{3}}+4 \left (-y+3 x \right )^{{1}/{3}}+16\right )+16 \ln \left (-64-y+3 x \right )+12 \left (-y+3 x \right )^{{1}/{3}}-c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.189 (sec). Leaf size: 55

DSolve[D[y[x],x]==(3*x-y[x])^(1/3)-1,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\frac {3}{2} (3 x-y(x))^{2/3}+12 \sqrt [3]{3 x-y(x)}+48 \log \left (\sqrt [3]{3 x-y(x)}-4\right )+x=c_1,y(x)\right ] \]