60.2.126 problem 702

Internal problem ID [10713]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 702
Date solved : Monday, January 27, 2025 at 09:29:19 PM
CAS classification : [[_homogeneous, `class D`], _Riccati]

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

✓ Solution by Maple

Time used: 0.060 (sec). Leaf size: 35

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

\[ y = \tan \left (\int \frac {x \ln \left (x \right )}{{\mathrm e}^{x}-x}d x +\int \frac {x}{{\mathrm e}^{x}-x}d x +c_{1} \right ) x \]

✓ Solution by Mathematica

Time used: 0.409 (sec). Leaf size: 53

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

\[ \text {Solve}\left [\int _1^{\frac {y(x)}{x}}\frac {1}{K[1]^2+1}dK[1]=\int _1^x\frac {K[2] (\log (K[2])+1)}{e^{K[2]}-K[2]}dK[2]+c_1,y(x)\right ] \]