60.2.113 problem 689

Internal problem ID [10700]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 689
Date solved : Monday, January 27, 2025 at 09:28:14 PM
CAS classification : [[_homogeneous, `class D`], _Riccati]

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

✓ Solution by Maple

Time used: 0.060 (sec). Leaf size: 25

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

\[ y = -\tanh \left ({\mathrm e}^{x +1}-{\mathrm e}^{2} \operatorname {Ei}_{1}\left (1-x \right )+c_{1} \right ) x \]

✓ Solution by Mathematica

Time used: 0.335 (sec). Leaf size: 54

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

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