67.1.1 problem Problem 1(a)

Internal problem ID [13948]
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)
Date solved : Tuesday, January 28, 2025 at 06:09:23 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 20

dsolve(diff(y(x),x)=y(x)*exp(x+y(x))*(x^2+1),y(x), singsol=all)
 

\[ \left (x^{2}-2 x +3\right ) {\mathrm e}^{x}+\operatorname {Ei}_{1}\left (y\right )+c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.543 (sec). Leaf size: 32

DSolve[D[y[x],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*}