Internal problem ID [2686]
Book: Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section: Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page
78
Problem number: 51.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], [_Abel, 2nd type, class A]]
Solve \begin {gather*} \boxed {y^{2}+\left ({\mathrm e}^{x}-y\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.019 (sec). Leaf size: 16
dsolve((y(x)^2)+( exp(x)-y(x))*diff(y(x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = -{\mathrm e}^{x} \LambertW \left (-{\mathrm e}^{-x} c_{1}\right ) \]
✓ Solution by Mathematica
Time used: 6.922 (sec). Leaf size: 306
DSolve[(y[x]^2)+( Exp[x]-y[x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {1}{9} 2^{2/3} \left (\frac {\left (\frac {e^x-\frac {3 e^{2 x}}{e^x-y(x)}}{\sqrt [3]{e^{3 x}}}+2\right ) \left (\frac {e^x \left (y(x)+2 e^x\right )}{\sqrt [3]{e^{3 x}} \left (e^x-y(x)\right )}+1\right ) \left (\left (\frac {e^x-\frac {3 e^{2 x}}{e^x-y(x)}}{\sqrt [3]{e^{3 x}}}-1\right ) \log \left (2^{2/3} \left (\frac {e^x-\frac {3 e^{2 x}}{e^x-y(x)}}{\sqrt [3]{e^{3 x}}}+2\right )\right )+\left (\frac {e^x \left (y(x)+2 e^x\right )}{\sqrt [3]{e^{3 x}} \left (e^x-y(x)\right )}+1\right ) \log \left (2^{2/3} \left (\frac {e^x \left (y(x)+2 e^x\right )}{\sqrt [3]{e^{3 x}} \left (e^x-y(x)\right )}+1\right )\right )-3\right )}{\frac {\left (y(x)+2 e^x\right )^3}{\left (e^x-y(x)\right )^3}-\frac {3 e^x \left (y(x)+2 e^x\right )}{\sqrt [3]{e^{3 x}} \left (e^x-y(x)\right )}-2}+e^{-2 x} \left (e^{3 x}\right )^{2/3} x\right )=c_1,y(x)\right ] \]