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For each of the following equations, find the general solution (perferably using imaginary numbers): y′′ −2y′...

For each of the following equations, find the general solution (perferably using imaginary numbers):

y′′ −2y′ −3y=3e2t;

y′′ +2y′ =3+sin(2t);

x2y′′ +7xy′ +5y=x;

x2y′′ +xy′ +4y=sin(lnx)+sin(2lnx);

y′′ +y=tcost.

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