2.2.13 Problem 14

Internal problem ID [9136]
Book : Second order enumerated odes
Section : section 2
Problem number : 14
Date solved : Sunday, March 30, 2025 at 02:23:07 PM
CAS classification : [_Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

✓ Maple. Time used: 0.005 (sec). Leaf size: 38

ode:=10*diff(diff(y(x),x),x)+(exp(x)+3*x)*diff(y(x),x)+3/sin(y(x))*exp(y(x))*diff(y(x),x)^2 = 0; 
dsolve(ode,y(x), singsol=all);
 

$${\int }_{}^y{\mathrm{e}}^{\frac{3\int {\mathrm{e}}^{\mathit{\text{\_b}}}\csc \left(\mathit{\text{\_b}}\right)d\mathit{\text{\_b}}}{10}}d\mathit{\text{\_b}}-c_1\int {\mathrm{e}}^{-\frac{3x^2}{20}-\frac{{\mathrm{e}}^x}{10}}dx-c_2=0$$

Maple trace

Methods for second order ODEs: 
--- Trying classification methods --- 
trying 2nd order Liouville 
<- 2nd_order Liouville successful
 

✓ Mathematica. Time used: 33.212 (sec). Leaf size: 71

ode=10*D[y[x],{x,2}]+(Exp[x]+3*x)*D[y[x],x]+3/Sin[y[x]]*Exp[y[x]]*(D[y[x],x])^2==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

$$y(x)\to \text{InverseFunction}[{\int }_1^{\mathrm{\#}\text{1}}\exp (-{\int }_1^{K[2]}-\frac{3}{10}{e}^{K[1]}\csc (K[1])dK[1])dK[2]\mathrm{\&}][{\int }_1^x-e^{\frac{1}{20}(-3K[3{]}^2-2e^{K[3]})}{c}_{1}dK[3]+c_2]$$

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((3*x + exp(x))*Derivative(y(x), x) + 3*exp(y(x))*Derivative(y(x), x)**2/sin(y(x)) + 10*Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

PolynomialDivisionFailed : couldnt reduce degree in a polynomial division algorithm when dividing [[], [], [], []] by [[ANP([mpq(1,1)], [mpq(1,1), mpq(0,1), mpq(1,1)], QQ)], [ANP([mpq(-1,1), mpq(-1,1)], [mpq(1,1), mpq(0,1), mpq(1,1)], QQ)]]. This can happen when its not possible to detect zero in the coefficient domain. The domain of computation is QQ<I>. Zero detection is guaranteed in this coefficient domain. This may indicate a bug in SymPy or the domain is user defined and doesnt implement zero detection properly.