60.2.409 problem 986

Internal problem ID [10996]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 986
Date solved : Monday, January 27, 2025 at 10:39:45 PM
CAS classification : [_Abel]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 33

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

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

✓ Solution by Mathematica

Time used: 0.248 (sec). Leaf size: 49

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

\begin{align*} y(x)\to x \left (\log (x)-\frac {1}{\sqrt {-2 x+c_1}}\right ) \\ y(x)\to x \left (\log (x)+\frac {1}{\sqrt {-2 x+c_1}}\right ) \\ y(x)\to x \log (x) \\ \end{align*}