60.1.344 problem 345

Internal problem ID [10358]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 345
Date solved : Monday, January 27, 2025 at 07:30:29 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]

\begin{align*} x \left (2 x^{2} y \ln \left (y\right )+1\right ) y^{\prime }-2 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.059 (sec). Leaf size: 36

dsolve(x*(2*x^2*y(x)*ln(y(x))+1)*diff(y(x),x)-2*y(x) = 0,y(x), singsol=all)
 

\[ y = {\mathrm e}^{\operatorname {RootOf}\left (2 \textit {\_Z} \,x^{2} {\mathrm e}^{2 \textit {\_Z}}-x^{2} {\mathrm e}^{2 \textit {\_Z}}+2 c_{1} x^{2}+2 \,{\mathrm e}^{\textit {\_Z}}\right )} \]

✓ Solution by Mathematica

Time used: 0.178 (sec). Leaf size: 35

DSolve[-2*y[x] + x*(1 + 2*x^2*Log[y[x]]*y[x])*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\frac {y(x)}{x^2}+2 \left (\frac {1}{2} y(x)^2 \log (y(x))-\frac {y(x)^2}{4}\right )=c_1,y(x)\right ] \]