Question

an integration factor of x dy/dx + (3+1) y = xe^-2x​

Answer 1

For

dx

dy

+P(x)y=Q(x) where &&P(x),Q(x)$$ are function of x

The integrating factor=e

∫P(x)dx

Here x

dx

dy

−y=x

3

dx

dy

−

x

y

=x

2

P(x)=−

x

1

Integrating Factor =e

∫−

x

1

dx

=e

−lnx

=e

lnx

−1

=e

ln

x

1

=

x

1