60.2.412 problem 989

Internal problem ID [10999]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 989
Date solved : Monday, January 27, 2025 at 10:39:54 PM
CAS classification : [[_homogeneous, `class D`], _Riccati]

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

✓ Solution by Maple

Time used: 0.075 (sec). Leaf size: 29

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

\[ y = \frac {\tan \left (\left (\int F \left (x \right ) x d x +c_{1} \right ) \sqrt {a b}\right ) x \sqrt {a b}}{a} \]

✓ Solution by Mathematica

Time used: 0.124 (sec). Leaf size: 42

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

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