Internal problem ID [15003]
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: 96.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {{\mathrm e}^{y}-{\mathrm e}^{4 y} y^{\prime }=1} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 33
dsolve(exp(y(x))=exp(4*y(x))*diff(y(x),x)+1,y(x), singsol=all)
\[ x -\frac {{\mathrm e}^{3 y}}{3}-\frac {{\mathrm e}^{2 y}}{2}-{\mathrm e}^{y}-\ln \left ({\mathrm e}^{y}-1\right )+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.366 (sec). Leaf size: 48
DSolve[Exp[y[x]]==Exp[4*y[x]]*y'[x]+1,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \text {InverseFunction}\left [\frac {1}{6} e^{\text {$\#$1}} \left (3 e^{\text {$\#$1}}+2 e^{2 \text {$\#$1}}+6\right )+\log \left (e^{\text {$\#$1}}-1\right )\&\right ][x+c_1] \\ y(x)\to 0 \\ \end{align*}