57.1.61 problem 61

Internal problem ID [9045]
Book : First order enumerated odes
Section : section 1
Problem number : 61
Date solved : Sunday, March 30, 2025 at 02:00:12 PM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

\begin{align*} y^{\prime }&=\left (1+6 x +y\right )^{{1}/{3}} \end{align*}

✓ Maple. Time used: 0.009 (sec). Leaf size: 79

ode:=diff(y(x),x) = (1+6*x+y(x))^(1/3); 
dsolve(ode,y(x), singsol=all);
 

\[ x -\frac {3 \left (1+6 x +y\right )^{{2}/{3}}}{2}+36 \ln \left (\left (1+6 x +y\right )^{{2}/{3}}-6 \left (1+6 x +y\right )^{{1}/{3}}+36\right )-72 \ln \left (6+\left (1+6 x +y\right )^{{1}/{3}}\right )-36 \ln \left (217+y+6 x \right )+18 \left (1+6 x +y\right )^{{1}/{3}}-c_1 = 0 \]

✓ Mathematica. Time used: 0.241 (sec). Leaf size: 66

ode=D[y[x],x]==(1+6*x+y[x])^(1/3); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\frac {1}{6} \left (y(x)-9 (y(x)+6 x+1)^{2/3}+108 \sqrt [3]{y(x)+6 x+1}-648 \log \left (\sqrt [3]{y(x)+6 x+1}+6\right )+6 x+1\right )-\frac {y(x)}{6}=c_1,y(x)\right ] \]

✓ Sympy. Time used: 0.899 (sec). Leaf size: 49

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-(6*x + y(x) + 1)**(1/3) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ C_{1} + x - \frac {3 \left (6 x + y{\left (x \right )} + 1\right )^{\frac {2}{3}}}{2} + 18 \sqrt [3]{6 x + y{\left (x \right )} + 1} - 108 \log {\left (\sqrt [3]{6 x + y{\left (x \right )} + 1} + 6 \right )} = 0 \]