Question

Subject differential equation
Day. Month.
Year. ..
(y-secx
) dx + tanxdy...o​

Answer 1

`(y-\sec x)\,\mathrm dx+\tan x\,\mathrm dy=0`

Divide both side by
`\mathrm dx` and rearrange terms to get a linear ODE;

`\tan x(\mathrm dy)/(\mathrm dx)+y=\sec x`

Multiply both sides by
`\cos x`:

`\sin x(\mathrm dy)/(\mathrm dx)+\cos x\,y=1`

The left side can be condensed as the derivative of a product:

`(\mathrm d)/(\mathrm dx)(\sin x\,y)=1`

Integrate both sides, then solve for
`y`:

`\sin x\,y=x+C\implies\boxed{y(x)=x\csc x+C\csc x}`