Internal problem ID [2202]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _dAlembert]
Solve \begin {gather*} \boxed {\frac {y^{\prime }}{y}-\frac {2 \ln \relax (y)}{x}-\frac {-2 \ln \relax (x )+1}{x}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = {\mathrm e}] \end {align*}
✓ Solution by Maple
Time used: 0.062 (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)
\[ y \relax (x ) = x \,{\mathrm e}^{x^{2}} \]
✓ Solution by Mathematica
Time used: 0.225 (sec). Leaf size: 12
DSolve[{y'[x]/y[x]-2/x*Log[y[x]]==1/x*(1-2*Log[x]),{y[1]==Exp[1]}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{x^2} x \\ \end{align*}