60.2.278 problem 854

Internal problem ID [10865]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 854
Date solved : Tuesday, January 28, 2025 at 05:26:40 PM
CAS classification : [NONE]

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

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 21

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

\[ y = \frac {{\mathrm e}^{-\frac {3 x}{x^{3}+3 c_{1}}}}{x} \]

✓ Solution by Mathematica

Time used: 0.348 (sec). Leaf size: 31

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

\begin{align*} y(x)\to \frac {e^{-\frac {3 x}{x^3+3 c_1}}}{x} \\ y(x)\to \frac {1}{x} \\ \end{align*}