Solution of differential equation dy/dx=(4x+y+1)^2

[installer2001]

hello genius guys,
can u people tell me the solution of differential equation dy/dx=(4x+y+1)^2

plz replyy
thz in advance

 

[argenes]

Re: reply reply plz

You can solve this DE by substitution method.
Let 4x+y+1=v
Then y=v-4x-1
--> dy/dx=dv/dx-4
the DE becomes
dv/dx=v²+4
which is a separable DE dv/(v²+4) =dx

Integrating both sides and simplifying we have
v=2 tan (2x+C)

therefore y=tan (2x+C) - 4x -1 is the general solution.

(Please check if there is any algebraic errors!!!)