57.1.62 problem 62

Internal problem ID [9046]
Book : First order enumerated odes
Section : section 1
Problem number : 62
Date solved : Sunday, March 30, 2025 at 02:00:15 PM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

\begin{align*} y^{\prime }&=\left (1+6 x +y\right )^{{1}/{4}} \end{align*}

✓ Maple. Time used: 0.010 (sec). Leaf size: 109

ode:=diff(y(x),x) = (1+6*x+y(x))^(1/4); 
dsolve(ode,y(x), singsol=all);
 

\[ x +216 \ln \left (-y-6 x +1295\right )+12 \sqrt {1+6 x +y}+216 \ln \left (\sqrt {1+6 x +y}-36\right )-216 \ln \left (\sqrt {1+6 x +y}+36\right )-144 \left (1+6 x +y\right )^{{1}/{4}}-432 \ln \left (\left (1+6 x +y\right )^{{1}/{4}}-6\right )+432 \ln \left (6+\left (1+6 x +y\right )^{{1}/{4}}\right )-\frac {4 \left (1+6 x +y\right )^{{3}/{4}}}{3}-c_1 = 0 \]

✓ Mathematica. Time used: 0.354 (sec). Leaf size: 79

ode=D[y[x],x]==(1+6*x+y[x])^(1/4); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\frac {1}{6} \left (y(x)-8 (y(x)+6 x+1)^{3/4}+72 \sqrt {y(x)+6 x+1}-864 \sqrt [4]{y(x)+6 x+1}+5184 \log \left (\sqrt [4]{y(x)+6 x+1}+6\right )+6 x+1\right )-\frac {y(x)}{6}=c_1,y(x)\right ] \]

✓ Sympy. Time used: 1.015 (sec). Leaf size: 63

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-(6*x + y(x) + 1)**(1/4) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ C_{1} + x - \frac {4 \left (6 x + y{\left (x \right )} + 1\right )^{\frac {3}{4}}}{3} - 144 \sqrt [4]{6 x + y{\left (x \right )} + 1} + 12 \sqrt {6 x + y{\left (x \right )} + 1} + 864 \log {\left (\sqrt [4]{6 x + y{\left (x \right )} + 1} + 6 \right )} = 0 \]