28.1.89 problem 92

Internal problem ID [4395]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page 78
Problem number : 92
Date solved : Tuesday, March 04, 2025 at 06:39:05 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _dAlembert]

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

✓ Maple. Time used: 0.010 (sec). Leaf size: 69

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

\begin{align*} y \left (x \right ) &= 1+\sqrt {4 c_{1} x +1}+\ln \left (2\right )-\ln \left (\frac {1+\sqrt {4 c_{1} x +1}}{x}\right ) \\ y \left (x \right ) &= 1-\sqrt {4 c_{1} x +1}+\ln \left (2\right )-\ln \left (\frac {1-\sqrt {4 c_{1} x +1}}{x}\right ) \\ \end{align*}

✓ Mathematica. Time used: 0.1 (sec). Leaf size: 34

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

\[ \text {Solve}\left [W\left (-2 x e^{-y(x)}\right )-\log \left (W\left (-2 x e^{-y(x)}\right )+2\right )+y(x)=c_1,y(x)\right ] \]

✓ Sympy. Time used: 1.187 (sec). Leaf size: 32

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

\[ C_{1} + y{\left (x \right )} - \log {\left (W\left (- 2 x e^{- y{\left (x \right )}}\right ) + 2 \right )} + W\left (- 2 x e^{- y{\left (x \right )}}\right ) = 0 \]