60.1.224 problem 229

Internal problem ID [10238]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 229
Date solved : Sunday, March 30, 2025 at 03:33:32 PM
CAS classification : [[_homogeneous, `class C`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (12 y-5 x -8\right ) y^{\prime }-5 y+2 x +3&=0 \end{align*}

✓ Maple. Time used: 0.184 (sec). Leaf size: 32

ode:=(12*y(x)-5*x-8)*diff(y(x),x)-5*y(x)+2*x+3 = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {-\sqrt {\left (x +4\right )^{2} c_1^{2}+24}+\left (5 x +8\right ) c_1}{12 c_1} \]

✓ Mathematica. Time used: 0.139 (sec). Leaf size: 77

ode=(12*y[x]-5*x-8)*D[y[x],x]-5*y[x]+2*x+3==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to \frac {1}{12} \left (-i \sqrt {-x^2-8 x-16 (4+9 c_1)}+5 x+8\right ) \\ y(x)\to \frac {1}{12} \left (i \sqrt {-x^2-8 x-16 (4+9 c_1)}+5 x+8\right ) \\ \end{align*}

✓ Sympy. Time used: 2.237 (sec). Leaf size: 48

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*x + (-5*x + 12*y(x) - 8)*Derivative(y(x), x) - 5*y(x) + 3,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = \frac {5 x}{12} - \frac {\sqrt {C_{1} + x^{2} + 8 x}}{12} + \frac {2}{3}, \ y{\left (x \right )} = \frac {5 x}{12} + \frac {\sqrt {C_{1} + x^{2} + 8 x}}{12} + \frac {2}{3}\right ] \]