29.7.3 problem 178

Internal problem ID [4778]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 7
Problem number : 178
Date solved : Monday, January 27, 2025 at 09:37:26 AM
CAS classification : [_rational, [_1st_order, `_with_symmetry_[F(x),G(x)]`], _Riccati]

\begin{align*} x y^{\prime }+b x +\left (2+a x y\right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 80

dsolve(x*diff(y(x),x)+b*x+(2+a*x*y(x))*y(x) = 0,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {-2 b a c_{1} x -i \sqrt {b}\, {\mathrm e}^{-2 i \sqrt {a}\, \sqrt {b}\, x} \sqrt {a}\, x -2 i c_{1} \sqrt {a}\, \sqrt {b}-{\mathrm e}^{-2 i \sqrt {a}\, \sqrt {b}\, x}}{x a \left (2 i c_{1} \sqrt {a}\, \sqrt {b}+{\mathrm e}^{-2 i \sqrt {a}\, \sqrt {b}\, x}\right )} \]

✓ Solution by Mathematica

Time used: 3.018 (sec). Leaf size: 43

DSolve[x D[y[x],x]+b x+(2+a x y[x])y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {1}{a x}-\sqrt {\frac {b}{a}} \tan \left (a x \sqrt {\frac {b}{a}}-c_1\right ) \]