7.5.58 problem 58

Internal problem ID [162]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.6 (substitution and exact equations). Problems at page 72
Problem number : 58
Date solved : Saturday, March 29, 2025 at 04:37:33 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]

\begin{align*} x y^{\prime }-4 x^{2} y+2 y \ln \left (y\right )&=0 \end{align*}

✓ Maple. Time used: 0.065 (sec). Leaf size: 14

ode:=x*diff(y(x),x)-4*x^2*y(x)+2*y(x)*ln(y(x)) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{\frac {x^{4}+c_1}{x^{2}}} \]

✓ Mathematica. Time used: 0.221 (sec). Leaf size: 17

ode=x*D[y[x],x]-4*x^2*y[x]+2*y[x]*Log[ y[x] ]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^{x^2+\frac {c_1}{x^2}} \]

✓ Sympy. Time used: 1.110 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-4*x**2*y(x) + x*Derivative(y(x), x) + 2*y(x)*log(y(x)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = e^{\frac {C_{1} + x^{4}}{x^{2}}} \]