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 : Monday, January 27, 2025 at 09:14:06 AM
CAS classification : [[_1st_order, _with_linear_symmetries], _dAlembert]

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

✓ Solution by Maple

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

dsolve(2*x*diff(y(x),x) -y(x) = ln(diff(y(x),x)),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*}

✓ Solution by Mathematica

Time used: 0.100 (sec). Leaf size: 34

DSolve[2*x*D[y[x],x] -y[x] == Log[D[y[x],x]],y[x],x,IncludeSingularSolutions -> True]
 

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