Internal problem ID [14982]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 4. Equations with variables separable and equations reducible to them. Exercises
page 38
Problem number: 55.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {{\mathrm e}^{y} \left (x^{2}+1\right ) y^{\prime }-2 x \left ({\mathrm e}^{y}+1\right )=0} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 13
dsolve(exp(y(x))*(1+x^2)*diff(y(x),x)-2*x*(1+exp(y(x)))=0,y(x), singsol=all)
\[ y \left (x \right ) = \ln \left (c_{1} x^{2}+c_{1} -1\right ) \]
✓ Solution by Mathematica
Time used: 0.638 (sec). Leaf size: 27
DSolve[Exp[y[x]]*(1+x^2)*y'[x]-2*x*(1+Exp[y[x]])==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \log \left (-1+e^{c_1} \left (x^2+1\right )\right ) \\ y(x)\to i \pi \\ \end{align*}