60.2.112 problem 688

Internal problem ID [10699]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 688
Date solved : Monday, January 27, 2025 at 09:28:10 PM
CAS classification : [[_homogeneous, `class D`], _Riccati]

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

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 42

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

\[ y = \tan \left (\frac {\left (x^{2}+2 x -3\right ) {\mathrm e}^{\frac {x +1}{x -1}}}{2}+4 \,{\mathrm e} \,\operatorname {Ei}_{1}\left (-\frac {2}{x -1}\right )+c_{1} \right ) x \]

✓ Solution by Mathematica

Time used: 0.283 (sec). Leaf size: 55

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

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