Internal problem ID [14981]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }-a^{y+x}=0} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 22
dsolve(diff(y(x),x)=a^(x+y(x)),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\ln \left (-\frac {1}{c_{1} \ln \left (a \right )+a^{x}}\right )}{\ln \left (a \right )} \]
✓ Solution by Mathematica
Time used: 3.796 (sec). Leaf size: 24
DSolve[y'[x]==a^(x+y[x]),y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {\log \left (-a^x-c_1 \log (a)\right )}{\log (a)} \]