Question

solve the differential equation cosxdy/dx+4ysinx=4√y secx​

Answer 1

Answer:

cosx.

dx

dy

+ysinx=sec

2

x

dx

dy

+ytanx=sec

3

x

Hence the integrating factor is

IF=e

∫tanx.dx

=e

ln∣secx∣

=secx

secx

dx

dy

+ysecxtanx=sec

4

x

secxdy+ysecxtanxdx=sec

4

xdx

∫d(ysecx)=∫sec

4

xdx

ysecx=∫sec

2

x(1+tan

2

x)dx

ysecx=∫sec

2

x+∫sec

2

xtan

2

xdx

ysecx=tanx+∫sec

2

xtan

2

xdx

Let tanx=t

sec

2

xdx=dt

Hence

ysecx=tanx+∫t

2

dx

ysecx=tanx+

3

t

3

+C

ysecx=tanx+

3

tan

3

x

+C

Answer 2

this is the answer for this question