15.3.17 problem 17

Internal problem ID [2910]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 7, page 28
Problem number : 17
Date solved : Tuesday, March 04, 2025 at 03:27:19 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

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

With initial conditions

\begin{align*} y \left (-2\right )&=1 \end{align*}

✓ Maple. Time used: 1.705 (sec). Leaf size: 77

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

\[ y = \frac {\left (-x -2\right ) {\operatorname {RootOf}\left (-1+\left (x^{5}+10 x^{4}+40 x^{3}+80 x^{2}+80 x +32\right ) \textit {\_Z}^{25}+\left (-5 x^{5}-50 x^{4}-200 x^{3}-400 x^{2}-400 x -160\right ) \textit {\_Z}^{20}\right )}^{5}}{2}+\frac {3 x}{2}+\frac {9}{2} \]

✓ Mathematica. Time used: 63.41 (sec). Leaf size: 850

ode=(3*x+2*y[x]+3)-(x+2*y[x]-1)*D[y[x],x]==0; 
ic={y[-2]==1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} \text {Solution too large to show}\end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(3*x - (x + 2*y(x) - 1)*Derivative(y(x), x) + 2*y(x) + 3,0) 
ics = {y(-2): 1} 
dsolve(ode,func=y(x),ics=ics)
 

ValueError : Couldnt solve for initial conditions