69.12.34 problem 308

Internal problem ID [18187]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 12. Miscellaneous problems. Exercises page 93
Problem number : 308
Date solved : Thursday, October 02, 2025 at 03:08:20 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (5 x -7 y+1\right ) y^{\prime }+x +y-1&=0 \end{align*}

✓ Maple. Time used: 0.367 (sec). Leaf size: 55

ode:=(5*x-7*y(x)+1)*diff(y(x),x)-1+x+y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {2 c_1 \operatorname {RootOf}\left (-7+\textit {\_Z}^{4}+\left (16 c_1 x -8 c_1 \right ) \textit {\_Z}^{3}\right )^{3} x -1}{2 \operatorname {RootOf}\left (-7+\textit {\_Z}^{4}+\left (16 c_1 x -8 c_1 \right ) \textit {\_Z}^{3}\right )^{3} c_1} \]

✓ Mathematica. Time used: 60.206 (sec). Leaf size: 4942

ode=(5*x-7*y[x]+1)*D[y[x],x]+(x+y[x]-1)==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Too large to display

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x + (5*x - 7*y(x) + 1)*Derivative(y(x), x) + y(x) - 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out