57.1.67 problem 67

Internal problem ID [9051]
Book : First order enumerated odes
Section : section 1
Problem number : 67
Date solved : Monday, January 27, 2025 at 05:31:31 PM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

\begin{align*} y^{\prime }&=10+{\mathrm e}^{x +y} \end{align*}

✓ Solution by Maple

Time used: 0.047 (sec). Leaf size: 26

dsolve(diff(y(x),x)=10+exp(x+y(x)),y(x), singsol=all)
 

\[ y = -x +\ln \left (11\right )+\ln \left (\frac {{\mathrm e}^{11 x}}{-{\mathrm e}^{11 x}+c_{1}}\right ) \]

✓ Solution by Mathematica

Time used: 3.263 (sec). Leaf size: 42

DSolve[D[y[x],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*}