58.1.16 problem 16

Internal problem ID [9087]
Book : Second order enumerated odes
Section : section 1
Problem number : 16
Date solved : Wednesday, March 05, 2025 at 07:19:27 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} {y^{\prime \prime }}^{2}+y^{\prime }&=1 \end{align*}

✓ Maple. Time used: 0.195 (sec). Leaf size: 30

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

\begin{align*} y &= x +c_{1} \\ y &= -\frac {1}{12} x^{3}+\frac {1}{2} c_{1} x^{2}-c_{1}^{2} x +x +c_{2} \\ \end{align*}

✓ Mathematica. Time used: 0.025 (sec). Leaf size: 67

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

\begin{align*} y(x)\to -\frac {x^3}{12}-\frac {c_1 x^2}{4}+x-\frac {c_1{}^2 x}{4}+c_2 \\ y(x)\to -\frac {x^3}{12}+\frac {c_1 x^2}{4}+x-\frac {c_1{}^2 x}{4}+c_2 \\ \end{align*}

✓ Sympy. Time used: 0.907 (sec). Leaf size: 24

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) + Derivative(y(x), (x, 2))**2 - 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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