ODE system phase plot with solutions

Hello

I need to plot ODE solve on These Quiver lines

here is my code for arrows plot

clc;clear;close all;clear global

x=-.5:0.05:.5;lamda=-.25:.01:.25;

[X,L]=meshgrid(x,lamda);

Dx1=-X.^4+L;
Dl=-.5*(abs(X).^3);

figure()
quiver(X,L,Dx1,Dl,2)
title('System 1')
xlabel('X');ylabel('\lambda')

hold on

and here is the plot

how to plot the true line of some solutions??