Internal problem ID [15057]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 6. Linear equations of the first order. The Bernoulli equation. Exercises page
54
Problem number: 164.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]
\[ \boxed {\left (1+x^{2}+y^{2}\right ) y^{\prime }+y x=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 113
dsolve((x^2+y(x)^2+1)*diff(y(x),x)+x*y(x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \sqrt {-x^{2}-1-\sqrt {x^{4}+2 x^{2}-4 c_{1}}} \\ y \left (x \right ) &= \sqrt {-x^{2}-1+\sqrt {x^{4}+2 x^{2}-4 c_{1}}} \\ y \left (x \right ) &= -\sqrt {-x^{2}-1-\sqrt {x^{4}+2 x^{2}-4 c_{1}}} \\ y \left (x \right ) &= -\sqrt {-x^{2}-1+\sqrt {x^{4}+2 x^{2}-4 c_{1}}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 2.437 (sec). Leaf size: 146
DSolve[(x^2+y[x]^2+1)*y'[x]+x*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {-x^2-\sqrt {x^4+2 x^2+1+4 c_1}-1} \\ y(x)\to \sqrt {-x^2-\sqrt {x^4+2 x^2+1+4 c_1}-1} \\ y(x)\to -\sqrt {-x^2+\sqrt {x^4+2 x^2+1+4 c_1}-1} \\ y(x)\to \sqrt {-x^2+\sqrt {x^4+2 x^2+1+4 c_1}-1} \\ y(x)\to 0 \\ \end{align*}