29.16.2 problem 445

Internal problem ID [5043]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 16
Problem number : 445
Date solved : Sunday, March 30, 2025 at 06:31:48 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (3-x +y\right ) y^{\prime }&=11-4 x +3 y \end{align*}

✓ Maple. Time used: 0.076 (sec). Leaf size: 30

ode:=(3-x+y(x))*diff(y(x),x) = 11-4*x+3*y(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\left (2 x -5\right ) \operatorname {LambertW}\left (-c_1 \left (x -2\right )\right )+x -2}{\operatorname {LambertW}\left (-c_1 \left (x -2\right )\right )} \]

✓ Mathematica. Time used: 1.308 (sec). Leaf size: 179

ode=(3-x+y[x])D[y[x],x]==11-4 x+3 y[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\frac {(-2)^{2/3} \left (-2 x \log \left (\frac {3 (-2)^{2/3} (-y(x)+2 x-5)}{-y(x)+x-3}\right )+(2 x-5) \log \left (-\frac {3 (-2)^{2/3} (x-2)}{-y(x)+x-3}\right )+5 \log \left (\frac {3 (-2)^{2/3} (-y(x)+2 x-5)}{-y(x)+x-3}\right )+y(x) \left (-\log \left (-\frac {3 (-2)^{2/3} (x-2)}{-y(x)+x-3}\right )+\log \left (\frac {3 (-2)^{2/3} (-y(x)+2 x-5)}{-y(x)+x-3}\right )-1\right )+x-3\right )}{9 (-y(x)+2 x-5)}=\frac {1}{9} (-2)^{2/3} \log (x-2)+c_1,y(x)\right ] \]

✓ Sympy. Time used: 1.365 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(4*x + (-x + y(x) + 3)*Derivative(y(x), x) - 3*y(x) - 11,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = 2 x + e^{C_{1} + W\left (\left (x - 2\right ) e^{- C_{1}}\right )} - 5 \]