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Here's the problem:

Solve y'-4y=9e^(7t) with y(0)=5

p(t)=-4

mu(t)=e^(int[-4dt])=e^(-4t)

multiplying both sides by mu(t)

e^(-4t)(y'-4y)=9e^(3t)

Dt(e^(-4t)y)=9e^(3t)

e^(-4t)y=3e^(3t)+c

y=(3e^(3t))/(e^(-4t))+c/e^(-4t)

now when y(0)=5

5=3+c

c=2

so y=(3e^(3t))/(e^(-4t))+2

That's not right, I also tried y=(3e^(3t))/(e^(-4t))(5/3)

and that's not right either. Any idea what I'm doing wrong?

Thanks.

Never mind, figured it out, I didn't divide c by the left side of the equation.

Solve y'-4y=9e^(7t) with y(0)=5

p(t)=-4

mu(t)=e^(int[-4dt])=e^(-4t)

multiplying both sides by mu(t)

e^(-4t)(y'-4y)=9e^(3t)

Dt(e^(-4t)y)=9e^(3t)

e^(-4t)y=3e^(3t)+c

y=(3e^(3t))/(e^(-4t))+c/e^(-4t)

now when y(0)=5

5=3+c

c=2

so y=(3e^(3t))/(e^(-4t))+2

That's not right, I also tried y=(3e^(3t))/(e^(-4t))(5/3)

and that's not right either. Any idea what I'm doing wrong?

Thanks.

Never mind, figured it out, I didn't divide c by the left side of the equation.

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