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Question: dsolve complicated?

Question:dsolve complicated?

Ratch 216 Maple
March 31 2012
1

The following is a differential equation with separable variables.  It is solved with dsolve and "manually".  Why is the dsolve solution so complicated?

Ratch

> 

restart
> 

interface(imaginaryunit = I)
> 

PAR := proc (A, B) options operator, arrow; A*B/(A+B) end proc
> 

EVALFC := proc (A) options operator, arrow; evalf(evalc(A)) end proc
> 

RAD := proc (A) options operator, arrow; (1/180)*A*Pi end proc; DEG := proc (A) options operator, arrow; 180*A/Pi end proc
> 

VL := proc (A, B) options operator, arrow; [A, y, y = B] end proc
> 

with(plots)
> 

with(DEtools)
> 

exp(x+1)*tan(y(x))+cos(y(x))*(diff(y(x), x)) = 0

exp(x+1)*tan(y(x))+cos(y(x))*(diff(y(x), x)) = 0

 (1)
> 

dsolve(exp(x+1)*tan(y(x))+cos(y(x))*(diff(y(x), x)) = 0)

y(x) = arctan(2*exp(RootOf(_Z+_Z*exp(2*_Z)+exp(x+1)+exp(1+x+2*_Z)-exp(2*_Z)+1+_C1*exp(1)+_C1*exp(1+2*_Z)))/(1+exp(2*RootOf(_Z+_Z*exp(2*_Z)+exp(x+1)+exp(1+x+2*_Z)-exp(2*_Z)+1+_C1*exp(1)+_C1*exp(1+2*_Z)))), (-exp(2*RootOf(_Z+_Z*exp(2*_Z)+exp(x+1)+exp(1+x+2*_Z)-exp(2*_Z)+1+_C1*exp(1)+_C1*exp(1+2*_Z)))+1)/(1+exp(2*RootOf(_Z+_Z*exp(2*_Z)+exp(x+1)+exp(1+x+2*_Z)-exp(2*_Z)+1+_C1*exp(1)+_C1*exp(1+2*_Z)))))

 (2)
> 

int(exp(x+1), x)+int(cos(y)/tan(y), y) = c

exp(x+1)+cos(y)+ln(csc(y)-cot(y)) = c

 (3)
> 

NULL



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