homogeneous differential equation

[dusty current]

[4y''+4y'+y=0] it is necessary to find a general and partial solution of the equation for [y(0)=4; y(2)=0]

[worthy vale]

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[brazen bear]

Well write the characteristic polynomial and find the roots you’ll have a general solution with the initial conditions you’ll have a particular solution

Basically there will be constants in the general solution which can be found with the initial conditions

And for it to be truly homogeneous you can divide by 4 on each side but here it won’t change anything to the solution so you can do however you want