10.5.13 problem 13

Internal problem ID [1205]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.6. Page 100
Problem number : 13
Date solved : Tuesday, March 04, 2025 at 12:19:25 PM
CAS classification : [[_homogeneous, `class A`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

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

With initial conditions

\begin{align*} y \left (1\right )&=3 \end{align*}

✓ Maple. Time used: 0.107 (sec). Leaf size: 19

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

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

✓ Mathematica. Time used: 0.484 (sec). Leaf size: 22

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

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

✓ Sympy. Time used: 1.312 (sec). Leaf size: 17

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

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