I mean the following ODE $$y''(x)+y'(x)=\exp (-2 x) y(x)^3.$$

Trying to solve it in version 13.1 on Windows 10 by

DSolve[y''[x] + y'[x] == Exp[-2 x]*y[x]^3, y[x], x]

, I obtain a huge incorrect result

{{y[x] -> 1/4 (-(E^( 1/2 (C[2] - Inactive[Integrate][(E^(-2 K[3]) (y[K[3]]^5 + 2 C[1] y[K[3]]^5 + 2 y[K[3]]^5 Inactive[Integrate][( E^(-2 K[1]) (y[K[1]] - Derivative[1][y][K[1]]) (-y[K[1]]^4 + E^(2 K[1]) y[K[1]] Derivative[1][y][K[1]] + E^(2 K[1]) Derivative[1][y][K[1]]^2))/( 2 y[K[1]]^3), {K[1], 1, K[3]}] + 8 E^(2 K[3]) C[1]^2 y[K[3]]^3 Sqrt[ 1 + 4 C[1] + ...

Pay your attention to Inactive[ Integrate][(E^(-2 K[1]) (y[K[1]] - Derivative[1][y][K[1]]) (-y[K[1]]^4 + E^(2 K[1]) y[K[1]] Derivative[1][y][K[1]] + E^(2 K[1]) Derivative[1][y][K[1]]^2))/(2 y[K[1]]^3), {K[1], 1, K[3]}]

in the above, where the function y[x] is expressed through itself and its derivative y'[x].

Next, the command

DSolve[{y''[x] + y'[x] == Exp[-2 x]*y[x]^3, y[0] == 1, y'[0] == -1},  y[x], x]

is running without any response for hours. Likely an infinite loop is created since the resourсes of my comp are not exhausted.

The change of the independent variable x by

DSolveChangeVariables[ Inactive[DSolve][{y''[x] + y'[x] == Exp[-2 x]*y[x]^3, y[0] == 1, 
y'[0] == -1}, y[x], x], u, t, t == Exp[-x]]

Inactive[DSolve][{t u[t]^3 == t u''[t], u[0] == 1, DSolve'DSolveChangeVariablesDump'd$18576[0][u[0]] == -1}, u[t], t]

produces at least two bugs: u[0]==1 instead of u[1]==1 and DSolve'DSolveChangeVariablesDump'd$18576[0][u[0]] == -1.

The questions arise: how to correctly solve this ODE? are there workarounds?