83.48.13 problem Ex 13 page 108

Internal problem ID [19526]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Book Solved Excercises. Chapter VII. Exact differential equations.
Problem number : Ex 13 page 108
Date solved : Thursday, March 13, 2025 at 02:47:43 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+y^{\prime }+{y^{\prime }}^{3}&=0 \end{align*}

✓ Maple. Time used: 0.029 (sec). Leaf size: 35

ode:=diff(diff(y(x),x),x)+diff(y(x),x)+diff(y(x),x)^3 = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y \left (x \right ) &= \arctan \left (\sqrt {c_{1} {\mathrm e}^{2 x}-1}\right )+c_{2} \\ y \left (x \right ) &= -\arctan \left (\sqrt {c_{1} {\mathrm e}^{2 x}-1}\right )+c_{2} \\ \end{align*}

✓ Mathematica. Time used: 60.07 (sec). Leaf size: 69

ode=D[y[x],{x,2}]+D[y[x],x]+D[y[x],x]^3==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to c_2-\arctan \left (e^{-c_1} \sqrt {e^{2 x}-e^{2 c_1}}\right ) \\ y(x)\to \arctan \left (e^{-c_1} \sqrt {e^{2 x}-e^{2 c_1}}\right )+c_2 \\ \end{align*}

✓ Sympy. Time used: 42.531 (sec). Leaf size: 112

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x)**3 + Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = C_{1} - \int \sqrt {- \frac {C_{2}}{C_{2} - e^{2 x}}}\, dx, \ y{\left (x \right )} = C_{1} + \int \sqrt {- \frac {C_{2}}{C_{2} - e^{2 x}}}\, dx, \ y{\left (x \right )} = C_{1} - \int \sqrt {- \frac {C_{2}}{C_{2} - e^{2 x}}}\, dx, \ y{\left (x \right )} = C_{1} + \int \sqrt {- \frac {C_{2}}{C_{2} - e^{2 x}}}\, dx, \ y{\left (x \right )} = C_{1} - \int \sqrt {- \frac {C_{2}}{C_{2} - e^{2 x}}}\, dx, \ y{\left (x \right )} = C_{1} + \int \sqrt {- \frac {C_{2}}{C_{2} - e^{2 x}}}\, dx\right ] \]