Internal problem ID [12212]
Book: APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A.
Dobrushkin. CRC Press 2015
Section: Chapter 2, First Order Equations. Problems page 149
Problem number: Problem 1(a).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }-y \,{\mathrm e}^{y+x} \left (x^{2}+1\right )=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 20
dsolve(diff(y(x),x)=y(x)*exp(x+y(x))*(x^2+1),y(x), singsol=all)
\[ \left (x^{2}-2 x +3\right ) {\mathrm e}^{x}+\operatorname {expIntegral}_{1}\left (y \left (x \right )\right )+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.859 (sec). Leaf size: 32
DSolve[y'[x]==y[x]*Exp[x+y[x]]*(x^2+1),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \text {InverseFunction}[\operatorname {ExpIntegralEi}(-\text {$\#$1})\&]\left [e^x \left (x^2-2 x+3\right )+c_1\right ] \\ y(x)\to 0 \\ \end{align*}