47.2.34 problem 32

Internal problem ID [7450]
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 : 32
Date solved : Sunday, March 30, 2025 at 12:07:17 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y^{\prime }&=-\frac {4 x +3 y+15}{2 x +y+7} \end{align*}

✓ Maple. Time used: 0.245 (sec). Leaf size: 226

ode:=diff(y(x),x) = -(4*x+3*y(x)+15)/(2*x+y(x)+7); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {-24 c_1 \left (x +3\right )^{2} \left (x +\frac {10}{3}\right ) \left (4 \sqrt {-4 c_1^{2} \left (x +3\right )^{6} \left (-\frac {1}{4}+\left (x +3\right )^{3} c_1 \right )}+4 \left (x^{3}+9 x^{2}+27 x +27\right ) c_1 \right )^{{2}/{3}}+i \left (-16 \left (x +3\right )^{6} c_1^{2}+\left (4 c_1 \,x^{3}+36 c_1 \,x^{2}+108 c_1 x +4 \sqrt {-4 c_1^{2} \left (x +3\right )^{6} \left (-\frac {1}{4}+\left (x +3\right )^{3} c_1 \right )}+108 c_1 \right )^{{4}/{3}}\right ) \sqrt {3}+16 \left (x +3\right )^{6} c_1^{2}+\left (4 c_1 \,x^{3}+36 c_1 \,x^{2}+108 c_1 x +4 \sqrt {-4 c_1^{2} \left (x +3\right )^{6} \left (-\frac {1}{4}+\left (x +3\right )^{3} c_1 \right )}+108 c_1 \right )^{{4}/{3}}}{8 \left (4 \sqrt {-4 c_1^{2} \left (x +3\right )^{6} \left (-\frac {1}{4}+\left (x +3\right )^{3} c_1 \right )}+4 \left (x^{3}+9 x^{2}+27 x +27\right ) c_1 \right )^{{2}/{3}} c_1 \left (x +3\right )^{2}} \]

✓ Mathematica. Time used: 60.068 (sec). Leaf size: 763

ode=D[y[x],x]==-(4*x+3*y[x]+15)/(2*x+y[x]+7); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) + (4*x + 3*y(x) + 15)/(2*x + y(x) + 7),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out