75.4.31 problem 96

Internal problem ID [16662]
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
Date solved : Monday, March 31, 2025 at 03:04:05 PM
CAS classification : [_quadrature]

\begin{align*} {\mathrm e}^{y}&={\mathrm e}^{4 y} y^{\prime }+1 \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 33

ode:=exp(y(x)) = exp(4*y(x))*diff(y(x),x)+1; 
dsolve(ode,y(x), singsol=all);
 

\[ x -\frac {{\mathrm e}^{3 y}}{3}-\frac {{\mathrm e}^{2 y}}{2}-{\mathrm e}^{y}-\ln \left ({\mathrm e}^{y}-1\right )+c_1 = 0 \]

✓ Mathematica. Time used: 0.4 (sec). Leaf size: 48

ode=Exp[y[x]]==Exp[4*y[x]]*D[y[x],x]+1; 
ic={}; 
DSolve[{ode,ic},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*}

✓ Sympy. Time used: 0.627 (sec). Leaf size: 32

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-exp(4*y(x))*Derivative(y(x), x) + exp(y(x)) - 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ x - \frac {e^{3 y{\left (x \right )}}}{3} - \frac {e^{2 y{\left (x \right )}}}{2} - e^{y{\left (x \right )}} - \log {\left (e^{y{\left (x \right )}} - 1 \right )} = C_{1} \]