Find an explicit solution (solved for y) of the given initial-value problem in terms of an integral function. dy/dx + 3y = e^x^5, y(2) = 5.

Question

asked Jul 3, 2020 141k views

1 Answer

Jason Foreman · Answer 1 · 2020-07-07T23:03:07+0000

Answer:

Explanation:

Using linear differential equation method:

\frac{\mathrm{d} y}{\mathrm{d} x}+3y=e^5^x

I.F.=
$e^{\int {Q} \, dx }$

I.F.=
$e^{\int {3} \, dx }$

I.F.=
e^(3x)

y(x)=
$(1)/(e^(3x))[\int {e^(5x)} \, dx+c]$

y(x)=
(e^(2x))/(5)+e^(-3x)* c

substituting x=2

c=
(25-e^4)/(5e^(-6))

Now

y=
(e^(2x))/(5)+e^(-3x)* (25-e^4)/(5e^(-6))