41.2.39 problem 37

Internal problem ID [8741]
Book : Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold Scientific. Singapore. 1995
Section : Chapter 1. First order differential equations. Section 1.2 Homogeneous equations problems. page 12
Problem number : 37
Date solved : Tuesday, September 30, 2025 at 05:48:07 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (x +4 y\right ) y^{\prime }&=2 x +3 y-5 \end{align*}

✓ Maple. Time used: 0.227 (sec). Leaf size: 33

ode:=(x+4*y(x))*diff(y(x),x) = 2*x+3*y(x)-5; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {-\operatorname {RootOf}\left (-3 \left (x -4\right ) c_1 \,\textit {\_Z}^{5}+2 \textit {\_Z}^{6}-1\right )+\left (x -5\right ) c_1}{c_1} \]

✓ Mathematica. Time used: 60.03 (sec). Leaf size: 805

ode=(x+4*y[x])*D[y[x],x]==2*x+3*y[x]-5; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.870 (sec). Leaf size: 36

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-2*x + (x + 4*y(x))*Derivative(y(x), x) - 3*y(x) + 5,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \log {\left (y{\left (x \right )} + 1 \right )} = C_{1} - \log {\left (\left (\frac {x - 4}{y{\left (x \right )} + 1} - 1\right )^{\frac {5}{6}} \sqrt [6]{\frac {x - 4}{y{\left (x \right )} + 1} + 2} \right )} \]