75.4.10 problem 55

Internal problem ID [16712]
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
Date solved : Tuesday, January 28, 2025 at 09:19:09 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.082 (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)
 

\[ y = \ln \left (c_{1} x^{2}+c_{1} -1\right ) \]

✓ Solution by Mathematica

Time used: 0.645 (sec). Leaf size: 27

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