17.1.23 problem 2(m)

Internal problem ID [4113]
Book : Theory and solutions of Ordinary Differential equations, Donald Greenspan, 1960
Section : Chapter 2. First order equations. Exercises at page 14
Problem number : 2(m)
Date solved : Tuesday, September 30, 2025 at 07:03:55 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y^{\prime }&=\frac {3 x -y+1}{3 y-x +5} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0 \\ \end{align*}

✓ Maple. Time used: 2.398 (sec). Leaf size: 113

ode:=diff(y(x),x) = (3*x-y(x)+1)/(3*y(x)-x+5); 
ic:=[y(0) = 0]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \frac {\left (-324+12 \sqrt {96 x^{3}+288 x^{2}+288 x +825}\right )^{{4}/{3}}-12 \left (-324+12 \sqrt {96 x^{3}+288 x^{2}+288 x +825}\right )^{{2}/{3}} x -84 \left (-324+12 \sqrt {96 x^{3}+288 x^{2}+288 x +825}\right )^{{2}/{3}}+576 x^{2}+1152 x +576}{36 \left (-324+12 \sqrt {96 x^{3}+288 x^{2}+288 x +825}\right )^{{2}/{3}}} \]

✓ Mathematica. Time used: 60.43 (sec). Leaf size: 341

ode=D[y[x],x]==(3*x-y[x]+1)/(3*y[x]-x+5); 
ic=y[0]==0; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {x \text {Root}\left [\text {$\#$1}^6 \left (1024 x^6+6144 x^5+15360 x^4+20480 x^3+15360 x^2+6144 x-58025\right )+\text {$\#$1}^4 \left (-384 x^4-1536 x^3-2304 x^2-1536 x-384\right )+\text {$\#$1}^3 \left (64 x^3+192 x^2+192 x+64\right )+\text {$\#$1}^2 \left (36 x^2+72 x+36\right )+\text {$\#$1} (-12 x-12)+1\&,1\right ]-5 \text {Root}\left [\text {$\#$1}^6 \left (1024 x^6+6144 x^5+15360 x^4+20480 x^3+15360 x^2+6144 x-58025\right )+\text {$\#$1}^4 \left (-384 x^4-1536 x^3-2304 x^2-1536 x-384\right )+\text {$\#$1}^3 \left (64 x^3+192 x^2+192 x+64\right )+\text {$\#$1}^2 \left (36 x^2+72 x+36\right )+\text {$\#$1} (-12 x-12)+1\&,1\right ]-1}{3 \text {Root}\left [\text {$\#$1}^6 \left (1024 x^6+6144 x^5+15360 x^4+20480 x^3+15360 x^2+6144 x-58025\right )+\text {$\#$1}^4 \left (-384 x^4-1536 x^3-2304 x^2-1536 x-384\right )+\text {$\#$1}^3 \left (64 x^3+192 x^2+192 x+64\right )+\text {$\#$1}^2 \left (36 x^2+72 x+36\right )+\text {$\#$1} (-12 x-12)+1\&,1\right ]} \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) - (3*x - y(x) + 1)/(-x + 3*y(x) + 5),0) 
ics = {y(0): 0} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out