12.5.25 problem 22

Internal problem ID [1649]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. Transformation of Nonlinear Equations into Separable Equations. Section 2.4 Page 68
Problem number : 22
Date solved : Tuesday, March 04, 2025 at 01:00:11 PM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

\begin{align*} y^{\prime }&=\frac {x y+y^{2}}{x^{2}} \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.050 (sec). Leaf size: 18

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

\[ y = \frac {2 x}{-2 \ln \left (x \right )-1+2 i \pi } \]

✓ Mathematica. Time used: 0.134 (sec). Leaf size: 25

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

\[ y(x)\to -\frac {2 i x}{2 i \log (x)+2 \pi +i} \]

✓ Sympy. Time used: 0.219 (sec). Leaf size: 14

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

\[ y{\left (x \right )} = \frac {x}{- \log {\left (x \right )} - \frac {1}{2} + i \pi } \]