35.8.17 problem 17

Internal problem ID [6224]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 13. Miscellaneous problems. page 466
Problem number : 17
Date solved : Wednesday, March 05, 2025 at 12:25:50 AM
CAS classification : [[_homogeneous, `class A`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Maple. Time used: 0.024 (sec). Leaf size: 51

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

\begin{align*} y &= \frac {-2 c_{1} x -\sqrt {5 c_{1}^{2} x^{2}+1}}{c_{1}} \\ y &= \frac {-2 c_{1} x +\sqrt {5 c_{1}^{2} x^{2}+1}}{c_{1}} \\ \end{align*}

✓ Mathematica. Time used: 0.461 (sec). Leaf size: 94

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

\begin{align*} y(x)\to -2 x-\sqrt {5 x^2+e^{2 c_1}} \\ y(x)\to -2 x+\sqrt {5 x^2+e^{2 c_1}} \\ y(x)\to -\sqrt {5} \sqrt {x^2}-2 x \\ y(x)\to \sqrt {5} \sqrt {x^2}-2 x \\ \end{align*}

✓ Sympy. Time used: 1.123 (sec). Leaf size: 32

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

\[ \left [ y{\left (x \right )} = - 2 x - \sqrt {C_{1} + 5 x^{2}}, \ y{\left (x \right )} = - 2 x + \sqrt {C_{1} + 5 x^{2}}\right ] \]