89.8.9 problem 11

Internal problem ID [24469]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 4. Additional topics on equations of first order and first degree. Exercises at page 66
Problem number : 11
Date solved : Thursday, October 02, 2025 at 10:40:00 PM
CAS classification : [[_homogeneous, `class C`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} 3 x +2 y+7+\left (2 x -y\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.153 (sec). Leaf size: 29

ode:=3*x+2*y(x)+7+(2*x-y(x))*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {2 c_1 x -\sqrt {7 \left (x +1\right )^{2} c_1^{2}+1}}{c_1} \]

✓ Mathematica. Time used: 0.075 (sec). Leaf size: 59

ode=(3*x+2*y[x]+7)+(2*x-y[x] )*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to 2 x-i \sqrt {-7 x^2-14 x-c_1}\\ y(x)&\to 2 x+i \sqrt {-7 x^2-14 x-c_1} \end{align*}

✓ Sympy. Time used: 1.183 (sec). Leaf size: 37

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

\[ \left [ y{\left (x \right )} = 2 x - \sqrt {C_{1} + 7 x^{2} + 14 x}, \ y{\left (x \right )} = 2 x + \sqrt {C_{1} + 7 x^{2} + 14 x}\right ] \]