Internal problem ID [578]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Miscellaneous problems, end of chapter 2. Page 133
Problem number: 11.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact]
\[ \boxed {y+\left ({\mathrm e}^{y}+x \right ) y^{\prime }=-x^{2}} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 39
dsolve(x^2+y(x)+(exp(y(x))+x)*diff(y(x),x) = 0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {-x^{3}-3 x \operatorname {LambertW}\left (\frac {{\mathrm e}^{-\frac {x^{3}+3 c_{1}}{3 x}}}{x}\right )-3 c_{1}}{3 x} \]
✓ Solution by Mathematica
Time used: 3.877 (sec). Leaf size: 42
DSolve[x^2+y[x]+(Exp[y[x]]+x)*y'[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -W\left (\frac {e^{-\frac {x^2}{3}+\frac {c_1}{x}}}{x}\right )-\frac {x^2}{3}+\frac {c_1}{x} \]