Internal problem ID [7383]
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]
\[ \boxed {y^{\prime }-{\mathrm e}^{x +y}=10} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 26
dsolve(diff(y(x),x)=10+exp(x+y(x)),y(x), singsol=all)
\[ y \left (x \right ) = -x +\ln \left (11\right )+\ln \left (\frac {{\mathrm e}^{11 x}}{-{\mathrm e}^{11 x}+c_{1}}\right ) \]
✓ Solution by Mathematica
Time used: 3.4 (sec). Leaf size: 42
DSolve[y'[x]==10+Exp[x+y[x]],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \log \left (-\frac {11 e^{10 x+11 c_1}}{-1+e^{11 (x+c_1)}}\right ) \\ y(x)\to \log \left (-11 e^{-x}\right ) \\ \end{align*}