40.3.4 problem 23 (h)

Internal problem ID [6608]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 5. Equations of first order and first degree (Exact equations). Supplemetary problems. Page 33
Problem number : 23 (h)
Date solved : Sunday, March 30, 2025 at 11:12:13 AM
CAS classification : [[_homogeneous, `class C`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} 2 x +3 y+4+\left (3 x +4 y+5\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.126 (sec). Leaf size: 32

ode:=2*x+3*y(x)+4+(3*x+4*y(x)+5)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {-\sqrt {\left (-1+x \right )^{2} c_1^{2}+8}+\left (-3 x -5\right ) c_1}{4 c_1} \]

✓ Mathematica. Time used: 0.131 (sec). Leaf size: 61

ode=(2*x+3*y[x]+4)+(3*x+4*y[x]+5)*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to \frac {1}{4} \left (-\sqrt {x^2-2 x+25+16 c_1}-3 x-5\right ) \\ y(x)\to \frac {1}{4} \left (\sqrt {x^2-2 x+25+16 c_1}-3 x-5\right ) \\ \end{align*}

✓ Sympy. Time used: 2.144 (sec). Leaf size: 49

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

\[ \left [ y{\left (x \right )} = - \frac {3 x}{4} - \frac {\sqrt {C_{1} + x^{2} - 2 x}}{4} - \frac {5}{4}, \ y{\left (x \right )} = - \frac {3 x}{4} + \frac {\sqrt {C_{1} + x^{2} - 2 x}}{4} - \frac {5}{4}\right ] \]