9.5.18 problem 22

Internal problem ID [2954]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 9, page 38
Problem number : 22
Date solved : Tuesday, September 30, 2025 at 06:11:48 AM
CAS classification : [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]

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

With initial conditions

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

✓ Maple. Time used: 0.105 (sec). Leaf size: 22

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

\[ y = \frac {-1-\sqrt {28 x^{3}+1}}{2 x^{2}} \]

✓ Mathematica. Time used: 0.615 (sec). Leaf size: 34

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

\begin{align*} y(x)&\to -\frac {\sqrt {\frac {1}{x^2}} \sqrt {28 x^3+1} x+1}{2 x^2} \end{align*}

✓ Sympy. Time used: 0.636 (sec). Leaf size: 20

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

\[ y{\left (x \right )} = \frac {- \sqrt {28 x^{3} + 1} - 1}{2 x^{2}} \]