82.18.20 problem Ex. 22

Internal problem ID [18771]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter III. Equations of the first order but not of the first degree. Examples on chapter III. page 38
Problem number : Ex. 22
Date solved : Monday, March 31, 2025 at 06:10:04 PM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

\begin{align*} {y^{\prime }}^{3}+m {y^{\prime }}^{2}&=a \left (y+m x \right ) \end{align*}

✓ Maple. Time used: 0.042 (sec). Leaf size: 85

ode:=diff(y(x),x)^3+m*diff(y(x),x)^2 = a*(y(x)+m*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = -m x +\frac {\left ({\mathrm e}^{\operatorname {RootOf}\left (2 \textit {\_Z} \,m^{2}+3 \,{\mathrm e}^{2 \textit {\_Z}}-8 m \,{\mathrm e}^{\textit {\_Z}}+2 c_1 a -2 x a +5 m^{2}\right )}-m \right )^{2} {\mathrm e}^{\operatorname {RootOf}\left (2 \textit {\_Z} \,m^{2}+3 \,{\mathrm e}^{2 \textit {\_Z}}-8 m \,{\mathrm e}^{\textit {\_Z}}+2 c_1 a -2 x a +5 m^{2}\right )}}{a} \]

✗ Mathematica

ode=D[y[x],x]^3+m*D[y[x],x]^2==a*(y[x]+m*x); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Timed out

✗ Sympy

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

Timed Out