Solve differential equationdy+5ydx=e^(-5x)dx

OlmekinjP

OlmekinjP

Answered question

2021-01-13

Solve differential equation dy+5ydx=e5xdx

Answer & Explanation

d2saint0

d2saint0

Skilled2021-01-14Added 89 answers

dydx+P(x)y=Q(x) (1)
where P(x) or Q(x) are constants or function of x alone
Integrating factor of (1) is
I.F.=eP(x)dx
Required solution is
y(I.F.)=Q(x)(I.F)dx+C
dy+(5y)dx=e5xdx
dydx+5y=e5x()
Since this equation is in the form dydx+P(x)y=Q(x) so it is linear ODE comparing () with dydx+P(x)y=Q(x) we get P(x)=5, Q(x)=e5x
So integrating factor is
I.F.=eP(x)dx
=e5dx
=e5x
y(I.F.)=Q(x)(I.F.)dx+c
y(e5x)=(e5x)(e5x)dx+C
y(e5x)=dx+C
=y(e5x)=x+C
y=x+Ce5x

Jeffrey Jordon

Jeffrey Jordon

Expert2021-12-25Added 2605 answers

Answer is given below (on video)

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