Solve differential equation y=e^(6x)−3x−2

CMIIh 2020-12-17 Answered
Solve differential equation y=e(6x)3x2
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Expert Answer

Luvottoq
Answered 2020-12-18 Author has 95 answers

y6y=7x+3
y=e6x3x2
y(x)+p(x)y=q(x)
p(x)=6
In order to solve the ordinary first order differential equation, we use integration factor that is:
μ(x)=ep(x)dx
μ(x)=e(6)dx
μ(x)=e61dx
μ(x)=e6x
Write the equation in the form
(μ(x)y)=μ(x)q(x)

So
(e6xy)=e6x(7x+3)
(e6xy)=6xe6x+3e6x
Solve
(e6xy)=7xe6x+3e6x
e6xy=7/36(6e6xxe6x)+3(1/6e6x)+c
e6xy=42/36e6xx7/36e6x3/6e6x+c
e6xy=42/36e6xx7/36e6x18/36e6x+c
e6xy=(42e6x25e6x)/36+c
y=42e6xx25e6x/(36e6x)+c

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