29.16.9 problem 452

Internal problem ID [5050]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 16
Problem number : 452
Date solved : Sunday, March 30, 2025 at 06:32:42 AM
CAS classification : [[_homogeneous, `class C`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Maple. Time used: 0.134 (sec). Leaf size: 32

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

\[ y = \frac {-\sqrt {11 \left (-1+x \right )^{2} c_1^{2}+1}+\left (3 x -2\right ) c_1}{c_1} \]

✓ Mathematica. Time used: 0.131 (sec). Leaf size: 63

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

\begin{align*} y(x)\to -i \sqrt {-11 x^2+22 x-4-c_1}+3 x-2 \\ y(x)\to i \sqrt {-11 x^2+22 x-4-c_1}+3 x-2 \\ \end{align*}

✓ Sympy. Time used: 1.925 (sec). Leaf size: 41

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

\[ \left [ y{\left (x \right )} = 3 x - \sqrt {C_{1} + 11 x^{2} - 22 x} - 2, \ y{\left (x \right )} = 3 x + \sqrt {C_{1} + 11 x^{2} - 22 x} - 2\right ] \]