75.4.9 problem 54

Internal problem ID [16711]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 4. Equations with variables separable and equations reducible to them. Exercises page 38
Problem number : 54
Date solved : Tuesday, January 28, 2025 at 09:19:07 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=a^{x +y} \end{align*}

✓ Solution by Maple

Time used: 0.075 (sec). Leaf size: 22

dsolve(diff(y(x),x)=a^(x+y(x)),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 3.794 (sec). Leaf size: 24

DSolve[D[y[x],x]==a^(x+y[x]),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {\log \left (-a^x-c_1 \log (a)\right )}{\log (a)} \]