40.2.25 problem 51

Internal problem ID [6603]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 4. Equations of first order and first degree (Variable separable). Supplemetary problems. Page 22
Problem number : 51
Date solved : Wednesday, March 05, 2025 at 01:30:25 AM
CAS classification : [[_homogeneous, `class C`], _Riccati]

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

✓ Maple. Time used: 0.006 (sec). Leaf size: 24

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

\[ y = -\frac {2 x}{3}-\frac {\sqrt {3}\, \tanh \left (2 \left (-x +c_1 \right ) \sqrt {3}\right )}{9} \]

✓ Mathematica. Time used: 0.164 (sec). Leaf size: 59

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

\begin{align*} y(x)\to \frac {1}{9} \left (-6 x-\frac {6}{\sqrt {3}+12 c_1 e^{4 \sqrt {3} x}}+\sqrt {3}\right ) \\ y(x)\to \frac {1}{9} \left (\sqrt {3}-6 x\right ) \\ \end{align*}

✓ Sympy. Time used: 0.373 (sec). Leaf size: 58

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

\[ y{\left (x \right )} = \frac {- 6 C_{1} x - \sqrt {3} C_{1} + 6 x e^{4 \sqrt {3} x} - \sqrt {3} e^{4 \sqrt {3} x}}{9 \left (C_{1} - e^{4 \sqrt {3} x}\right )} \]