60.2.414 problem 991

Internal problem ID [11001]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 991
Date solved : Monday, January 27, 2025 at 10:40:01 PM
CAS classification : [[_homogeneous, `class D`], _Riccati]

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

✓ Solution by Maple

Time used: 0.053 (sec). Leaf size: 29

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

\[ y = \frac {x \left (\sqrt {2}-2 \tanh \left (\left (\int F \left (x \right ) x d x +c_{1} \right ) \sqrt {2}\right )\right ) \sqrt {2}}{2} \]

✓ Solution by Mathematica

Time used: 0.115 (sec). Leaf size: 44

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

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