75.1.10 problem 11

Internal problem ID [16594]
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 : Thursday, March 13, 2025 at 08:25:25 AM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

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

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

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

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

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

ode=D[y[x],x]==(3*x-y[x])^(1/3)-1; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.921 (sec). Leaf size: 44

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-(3*x - y(x))**(1/3) + Derivative(y(x), x) + 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ C_{1} + x + \frac {3 \left (3 x - y{\left (x \right )}\right )^{\frac {2}{3}}}{2} + 12 \sqrt [3]{3 x - y{\left (x \right )}} + 48 \log {\left (\sqrt [3]{3 x - y{\left (x \right )}} - 4 \right )} = 0 \]