Question

give me the solution of the above questions

Answer 1

Explanation:



sin^−1(dy/dx)=x+y.∴sin(x+y)=dy/dx.

Let x+y=u.∴d/dx(x+y)=d/dx(u),i.e.,1+dy/dx=du/dx.

Subst.ing in the diff. eqn.,

sinu=du/dx−1,or,du/dx=1+sinu.

∴du/1+sinu=dx................[Separable Variable].

∴∫du/1+sinu=∫dx+c.

∴∫1−sinu/1−sin^2u×du=x+c,

or,∫1−sinu/cos^2u×du=x+c.

∴∫{1/cos^2u−sinu/cos^2u}du=x+c.

∴tanu−secu=x+c.

Letting u=x+y, we get the gen. soln. as under :

tan(x+y)−sec(x+y)=x+c.