20.4.47 problem Problem 65

Internal problem ID [3682]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 1, First-Order Differential Equations. Section 1.8, Change of Variables. page 79
Problem number : Problem 65
Date solved : Monday, January 27, 2025 at 07:54:43 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

\begin{align*} \frac {y^{\prime }}{y}-\frac {2 \ln \left (y\right )}{x}&=\frac {1-2 \ln \left (x \right )}{x} \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.030 (sec). Leaf size: 10

dsolve([diff(y(x),x)/y(x)-2/x*ln(y(x))=1/x*(1-2*ln(x)),y(1) = exp(1)],y(x), singsol=all)
 

\[ y \left (x \right ) = x \,{\mathrm e}^{x^{2}} \]

✓ Solution by Mathematica

Time used: 0.220 (sec). Leaf size: 12

DSolve[{D[y[x],x]/y[x]-2/x*Log[y[x]]==1/x*(1-2*Log[x]),{y[1]==Exp[1]}},y[x],x,IncludeSingularSolutions -> True]
 

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