i) the solution of dy/dx= ex (sinx + cosx) is- ii) the solution of sec2x tany dx + sec2y - Maths - Differential Equations

Question

i) the solution of dy/dx= ex (sinx + cosx) is-?
ii) the solution of sec2x tany dx + sec2y
tanx dy =0 is?

Manbar Singh · Accepted Answer

1
     dydx = exsin x + cos x⇒dy = exsin x + cos x dxIntegrating both sides, we get∫dy = ∫exsin x + cos x dx⇒y = ∫ex sin x dx + ∫ex cos x dx⇒y = sin x × ∫ exdx - ∫ddxsin x × ∫ex dx + ∫ex cos x dx⇒y = ex sin x - ∫ex cos x dx + ∫ex cos x dx⇒y = ex sin x + CKindly ask the remaining query in different thread

i) the solution of dy/dx= ex (sinx + cosx) is-? ii) the solution of sec2x tany dx + sec2y tanx dy =0 is?

i) the solution of dy/dx= e^x (sinx + cosx) is-?
ii) the solution of sec²x tany dx + sec²y tanx dy =0 is?