75.3.30 problem 31

Internal problem ID [19934]
Book : A short course on differential equations. By Donald Francis Campbell. Maxmillan company. London. 1907
Section : Chapter III. Ordinary differential equations of the first order and first degree. Exercises at page 33
Problem number : 31
Date solved : Thursday, October 02, 2025 at 05:03:12 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (5 x -2 y+7\right ) y^{\prime }&=x -3 y+2 \end{align*}

✓ Maple. Time used: 1.296 (sec). Leaf size: 76

ode:=(5*x-2*y(x)+7)*diff(y(x),x) = x-3*y(x)+2; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\frac {\operatorname {RootOf}\left (-\sqrt {14}\, \operatorname {arctanh}\left (\frac {\left (37+\textit {\_Z} +26 x \right ) \sqrt {14}}{91 x +119}\right )+7 \ln \left (\frac {2 \textit {\_Z}^{2}+104 x \textit {\_Z} +169 x^{2}+148 \textit {\_Z} +754 x +715}{\left (13 x +17\right )^{2}}\right )+14 \ln \left (13 x +17\right )+14 c_1 \right )}{13} \]

✓ Mathematica. Time used: 0.118 (sec). Leaf size: 88

ode=(5*x-2*y[x]+7)*D[y[x],x]==x-3*y[x]+2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [2 \sqrt {14} \text {arctanh}\left (\frac {\sqrt {\frac {2}{7}} (y(x)-9 x-12)}{-2 y(x)+5 x+7}\right )+14 \log \left (-\frac {2 \left (13 x^2+26 y(x)^2-4 (26 x+37) y(x)+58 x+55\right )}{(13 x+17)^2}\right )+28 \log (13 x+17)=91 c_1,y(x)\right ] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x + (5*x - 2*y(x) + 7)*Derivative(y(x), x) + 3*y(x) - 2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out