60.2.376 problem 953

Internal problem ID [10963]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 953
Date solved : Tuesday, January 28, 2025 at 05:37:18 PM
CAS classification : [NONE]

\begin{align*} y^{\prime }&=\frac {y \left (\ln \left (x \right )+\ln \left (y\right )-1+x \ln \left (x \right )^{2}+2 x \ln \left (y\right ) \ln \left (x \right )+x \ln \left (y\right )^{2}+x^{3} \ln \left (x \right )^{2}+2 x^{3} \ln \left (y\right ) \ln \left (x \right )+x^{3} \ln \left (y\right )^{2}+x^{4} \ln \left (x \right )^{2}+2 x^{4} \ln \left (y\right ) \ln \left (x \right )+x^{4} \ln \left (y\right )^{2}\right )}{x} \end{align*}

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 33

dsolve(diff(y(x),x) = y(x)*(ln(x)+ln(y(x))-1+x*ln(x)^2+2*x*ln(y(x))*ln(x)+x*ln(y(x))^2+x^3*ln(x)^2+2*x^3*ln(y(x))*ln(x)+x^3*ln(y(x))^2+x^4*ln(x)^2+2*x^4*ln(y(x))*ln(x)+x^4*ln(y(x))^2)/x,y(x), singsol=all)
 

\[ y = \frac {{\mathrm e}^{-\frac {20 x}{4 x^{5}+5 x^{4}+10 x^{2}+20 c_{1}}}}{x} \]

✓ Solution by Mathematica

Time used: 0.565 (sec). Leaf size: 43

DSolve[D[y[x],x] == ((-1 + Log[x] + x*Log[x]^2 + x^3*Log[x]^2 + x^4*Log[x]^2 + Log[y[x]] + 2*x*Log[x]*Log[y[x]] + 2*x^3*Log[x]*Log[y[x]] + 2*x^4*Log[x]*Log[y[x]] + x*Log[y[x]]^2 + x^3*Log[y[x]]^2 + x^4*Log[y[x]]^2)*y[x])/x,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {e^{-\frac {20 x}{4 x^5+5 x^4+10 x^2+20 c_1}}}{x} \\ y(x)\to \frac {1}{x} \\ \end{align*}