75.6.31 problem 164

Internal problem ID [16787]
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
Date solved : Tuesday, January 28, 2025 at 09:22:55 AM
CAS classification : [_rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]

\begin{align*} \left (1+x^{2}+y^{2}\right ) y^{\prime }+y x&=0 \end{align*}

✓ Solution by Maple

Time used: 0.064 (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 &= \sqrt {-x^{2}-1-\sqrt {x^{4}+2 x^{2}-4 c_{1}}} \\ y &= \sqrt {-x^{2}-1+\sqrt {x^{4}+2 x^{2}-4 c_{1}}} \\ y &= -\sqrt {-x^{2}-1-\sqrt {x^{4}+2 x^{2}-4 c_{1}}} \\ y &= -\sqrt {-x^{2}-1+\sqrt {x^{4}+2 x^{2}-4 c_{1}}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 2.513 (sec). Leaf size: 146

DSolve[(x^2+y[x]^2+1)*D[y[x],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*}