y'+5y'=3ex, y(0)=1

solve the IVP
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1 Answer

Do you mean y'+5y=3ex?

Multiply through by e5x:

e5xy'+5e5xy=3e6x,

(d/dx)(e5xy)=3e6x,

e5xy=3∫e6xdx,

e5xy=(3/6)e6x=½e6x+C,

y=½ex+Ce-5x.

y(0)=1=½+C, so C=½.

y=½(ex+e-5x).

CHECK

y'=½ex-(5/2)e-5x.

5y=(5/2)ex+(5/2)e-5x

y'+5y=3ex.

by Top Rated User (1.1m points)

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