29.36.29 problem 1100

Internal problem ID [5656]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 36
Problem number : 1100
Date solved : Sunday, March 30, 2025 at 09:53:24 AM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]

\begin{align*} {y^{\prime }}^{6}+f \left (x \right ) \left (y-a \right )^{4} \left (y-b \right )^{3}&=0 \end{align*}

✓ Maple. Time used: 0.147 (sec). Leaf size: 69

ode:=diff(y(x),x)^6+f(x)*(y(x)-a)^4*(y(x)-b)^3 = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \int _{}^{y}\frac {1}{\sqrt {\textit {\_a} -b}\, \left (\textit {\_a} -a \right )^{{2}/{3}}}d \textit {\_a} -\frac {\int _{}^{x}\left (-f \left (\textit {\_a} \right ) \left (y-b \right )^{3} \left (y-a \right )^{4}\right )^{{1}/{6}}d \textit {\_a}}{\sqrt {y-b}\, \left (y-a \right )^{{2}/{3}}}+c_1 = 0 \]

✓ Mathematica. Time used: 2.055 (sec). Leaf size: 561

ode=(D[y[x],x])^6 +f[x] (y[x]-a)^4 (y[x]-b)^3==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} \text {Solution too large to show}\end{align*}

✓ Sympy. Time used: 55.188 (sec). Leaf size: 367

from sympy import * 
x = symbols("x") 
a = symbols("a") 
b = symbols("b") 
y = Function("y") 
f = Function("f") 
ode = Eq((-a + y(x))**4*(-b + y(x))**3*f(x) + Derivative(y(x), x)**6,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \text {Solution too large to show} \]