85.12.8 problem 8

Internal problem ID [22502]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter two. First order and simple higher order ordinary differential equations. A Exercises at page 40
Problem number : 8
Date solved : Thursday, October 02, 2025 at 08:43:15 PM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 39

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

\begin{align*} y &= \frac {3+\sqrt {4 c_1 x +9}}{2 c_1} \\ y &= \frac {3-\sqrt {4 c_1 x +9}}{2 c_1} \\ \end{align*}

✓ Mathematica. Time used: 0.666 (sec). Leaf size: 83

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

\begin{align*} y(x)&\to \frac {1}{2} \left (3 e^{c_1}-e^{\frac {c_1}{2}} \sqrt {4 x+9 e^{c_1}}\right )\\ y(x)&\to \frac {1}{2} \left (e^{\frac {c_1}{2}} \sqrt {4 x+9 e^{c_1}}+3 e^{c_1}\right )\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 1.162 (sec). Leaf size: 41

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

\[ \left [ y{\left (x \right )} = \frac {3 C_{1}}{2} - \frac {\sqrt {C_{1} \left (9 C_{1} + 4 x\right )}}{2}, \ y{\left (x \right )} = \frac {3 C_{1}}{2} + \frac {\sqrt {C_{1} \left (9 C_{1} + 4 x\right )}}{2}\right ] \]