Internal problem ID [6630]
Book: First order enumerated odes
Section: section 1
Problem number: 67.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class C], _dAlembert]
Solve \begin {gather*} \boxed {y^{\prime }-10-{\mathrm e}^{x +y}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.086 (sec). Leaf size: 21
dsolve(diff(y(x),x)=10+exp(x+y(x)),y(x), singsol=all)
\[ y \relax (x ) = -x +\ln \left (\frac {11}{{\mathrm e}^{-11 x} c_{1}-1}\right ) \]
✓ Solution by Mathematica
Time used: 1.342 (sec). Leaf size: 39
DSolve[y'[x]==10+Exp[x+y[x]],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \log \left (-\frac {11 c_1 e^{10 x}}{-1+c_1 e^{11 x}}\right ) \\ y(x)\to \log \left (-11 e^{-x}\right ) \\ \end{align*}