60.1.280 problem 286

Internal problem ID [10294]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 286
Date solved : Sunday, March 30, 2025 at 03:44:01 PM
CAS classification : [[_homogeneous, `class C`], _rational]

\begin{align*} \left (2 y-3 x +1\right )^{2} y^{\prime }-\left (3 y-2 x -4\right )^{2}&=0 \end{align*}

✓ Maple. Time used: 0.403 (sec). Leaf size: 106

ode:=(2*y(x)-3*x+1)^2*diff(y(x),x)-(3*y(x)-2*x-4)^2 = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\left (-5 x +11\right ) {\operatorname {RootOf}\left (\left (20 c_1 \left (\left (5 x -11\right ) c_1 \right )^{{4}/{5}} x -44 c_1 \left (\left (5 x -11\right ) c_1 \right )^{{4}/{5}}\right ) \textit {\_Z}^{10}+\left (45 c_1 \left (\left (5 x -11\right ) c_1 \right )^{{4}/{5}} x -99 c_1 \left (\left (5 x -11\right ) c_1 \right )^{{4}/{5}}\right ) \textit {\_Z}^{5}-\textit {\_Z} -45 c_1 \left (\left (5 x -11\right ) c_1 \right )^{{4}/{5}} x +99 c_1 \left (\left (5 x -11\right ) c_1 \right )^{{4}/{5}}\right )}^{5}}{5}+x +\frac {3}{5} \]

✓ Mathematica. Time used: 60.202 (sec). Leaf size: 3501

ode=(2*y[x]-3*x+1)^2*D[y[x],x]-(3*y[x]-2*x-4)^2==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((-3*x + 2*y(x) + 1)**2*Derivative(y(x), x) - (-2*x + 3*y(x) - 4)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out