Internal problem ID [15071]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 7, Total differential equations. The integrating factor. Exercises page
61
Problem number: 182.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {\frac {x y}{\sqrt {x^{2}+1}}+2 y x -\frac {y}{x}+\left (\sqrt {x^{2}+1}+x^{2}-\ln \left (x \right )\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 64
dsolve(( x*y(x)/sqrt(1+x^2) + 2*x*y(x) -y(x)/x )+( sqrt(1+x^2) + x^2-ln(x) )*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} {\mathrm e}^{-\left (\int \frac {2 \sqrt {x^{2}+1}\, x^{2}+x^{2}-\sqrt {x^{2}+1}}{\sqrt {x^{2}+1}\, x \left (\sqrt {x^{2}+1}+x^{2}-\ln \left (x \right )\right )}d x \right )} \]
✓ Solution by Mathematica
Time used: 7.409 (sec). Leaf size: 94
DSolve[( x*y[x]/Sqrt[1+x^2] + 2*x*y[x] -y[x]/x )+( Sqrt[1+x^2] + x^2-Log[x] )*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 \exp \left (\int _1^x\frac {\sqrt {K[1]^2+1}-K[1]^2 \left (2 \sqrt {K[1]^2+1}+1\right )}{K[1] \left (\left (\sqrt {K[1]^2+1}+1\right ) K[1]^2-\sqrt {K[1]^2+1} \log (K[1])+1\right )}dK[1]\right ) \\ y(x)\to 0 \\ \end{align*}