Question

PLEASE SOLVE " dy/dx=sin(x+y)+cos(x+y) "

Answer 1

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Actually Welcome to the Concept of the Differential Equations,

Basically here we are going to use the Substitution as

x+y = p

thus we get as

1+dy/dx = dp/dx

dy/dx = dp/dx - 1

so we get as

dp/dx -1 = sinp + cosp

dp/dx = sinp + cosp +1

dp/ sinp + cosp + 1 = dx

integration on both sides we get as

lnl 1+tan(p/2)l = x + C

so we get as

ln l 1+tan(x+y/2) l = x+ C