Question: Solving ODEs without the Student package

As it says in the title, I would like to solve the following ODE numerically using forward Euler method, without using the Student Package.

 

(dy(t))/(dt)=t(1-0.3t)-(ty)(1+0.6t)

with initial condition y(0)=1. I want to solve it for up to t=1, and then plot both the solution by Euler's method and the solution by "dsolve" on the same graph so I can compare them.

 

Also, can I make a separate DEplot with t extending to 5?

 

Thanks in advance.

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