51.1.60 problem 60

Internal problem ID [10330]
Book : First order enumerated odes
Section : section 1
Problem number : 60
Date solved : Tuesday, September 30, 2025 at 07:19:35 PM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

\begin{align*} y^{\prime }&=\sqrt {1+6 x +y} \end{align*}

✓ Maple. Time used: 0.009 (sec). Leaf size: 57

ode:=diff(y(x),x) = (1+6*x+y(x))^(1/2); 
dsolve(ode,y(x), singsol=all);
 

\[ x -2 \sqrt {1+6 x +y}-6 \ln \left (-6+\sqrt {1+6 x +y}\right )+6 \ln \left (6+\sqrt {1+6 x +y}\right )+6 \ln \left (-35+y+6 x \right )-c_1 = 0 \]

✓ Mathematica. Time used: 8.225 (sec). Leaf size: 65

ode=D[y[x],x]==(1+6*x+y[x])^(1/2); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to 36 W\left (-\frac {1}{6} e^{\frac {1}{72} (-6 x-73+6 c_1)}\right ){}^2+72 W\left (-\frac {1}{6} e^{\frac {1}{72} (-6 x-73+6 c_1)}\right )-6 x+35\\ y(x)&\to 35-6 x \end{align*}

✓ Sympy. Time used: 0.553 (sec). Leaf size: 34

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

\[ C_{1} + x - 2 \sqrt {6 x + y{\left (x \right )} + 1} + 12 \log {\left (\sqrt {6 x + y{\left (x \right )} + 1} + 6 \right )} = 0 \]