p = dsolve('D2p+Dp/r=(r^2+c^2)^(1/2)')توی ' ' r نوشتم که البته اونجا یادم رفت تایپ کنم.
mhelp csng-1/3c^3log(2c/r)>> mhelp csgn
csgn - sign function for real and complex expressions
Calling Sequence
csgn(x)
csgn(1, x)
csgn(0, x, y)
Parameters
x - any algebraic expression
y - any algebraic expression
Description
- The csgn function is used to determine in which half-plane ("left" or "right")
the complex-valued expression or number x lies. It is defined by
/ 1 if Re(x) > 0 or Re(x) = 0 and Im(x) > 0
csgn(x) = <
\ -1 if Re(x) < 0 or Re(x) = 0 and Im(x) < 0
- The value of csgn(0) is controlled by the environment variable _Envsignum0.
The 3-argument calling sequence csgn(0, x, y) sets _Envsignum0 = y for the
duration of the call to csgn. See signum for further information.
- The decision of whether or not to perform many of the automatic symmetry
transformations in maple is based on the value of csgn. For example, if
csgn(x) = -1, the transformation sin(x) --> -sin(-x) is done.
- csgn uses signum to determine the signs of Re(x) and Im(x).
- The derivative of csgn is denoted by csgn(1, x). This is 0 for all
non-purely-imaginary numbers, and is undefined otherwise.
- For mathematical consistency, the value of csgn(0), as determined either by
the value of _Envsignum0 or by the third argument to csgn, should be either 0
(the default) or one of 1, -1, or undefined.
Examples
> csgn(1-2/3*I);
1
> csgn(exp(2*Pi/3*I));
-1
> csgn(Pi);
1
> diff(csgn(x), x);
csgn(1, x)
> csgn(1,-3+I);
0
See Also
evalc, sign, signum, inifcns, assumeاز نظر ریاضی معادل هستند؛ بنابراین مشکلی رو به وجود نمیارن.
غیر ممکنه که متلب همچین اشتباه فاحشی در ارائه جواب یه معادله دیفرانسیل بدون شرط داشته باشه.
در زیر بعضی از دستورهاش رو به کار بردم. در ساده سازی، یا از یک بیان به بیان دیگه درآوردن یک عبارت علاوه بر دستورهای دستکاری نمادین، یک مقدار درک ریاضی از اون مسأله هم نیازه.
>> p=dsolve('D2p+Dp/r=(r^2+c^2)^(1/2)','r')
p =
1/9*(r^2+c^2)^(3/2)+1/3*(r^2+c^2)^(1/2)*c^2-1/3*c^4/(c^2)^(1/2)*log((2*c^2+2*(c^2)^(1/2)*(r^2+c^2)^(1/2))/r)+C1*log(r)+C2
>> p=simple(p)
p =
1/9*(r^2+c^2)^(1/2)*r^2+4/9*(r^2+c^2)^(1/2)*c^2-1/3*c^3*log(2*c*(c+(r^2+c^2)^(1/2))/r)+C1*log(r)+C2
>> p=subs(p,'(r^2+c^2)^(1/2)','a')
p =
1/9*(a)*r^2+4/9*(a)*c^2-1/3*c^3*log(2*c*(c+(a))/r)+C1*log(r)+C2
>> p=collect(p,sym('a'))
p =
(4/9*c^2+1/9*r^2)*a+C2-1/3*c^3*log(2*c*(c+a)/r)+C1*log(r)
>> k1=sym('(4/9*c^2+1/9*r^2)*a')
k1 =
(4/9*c^2+1/9*r^2)*a
>> k2=p-k1
k2 =
C2-1/3*c^3*log(2*c*(c+a)/r)+C1*log(r)
>> k2=simplify(subs(k2,'C1','-1/3*c^3+C3'))
k2 =
C2-1/3*c^3*log(2)-1/3*c^3*log(c*(c+a)/r)-1/3*c^3*log(r)+log(r)*C3
>> k2=simple(k2)
k2 =
C2-1/3*c^3*log(2)-1/3*c^3*log(c*(c+a)/r)-1/3*c^3*log(r)+log(r)*C3
>> k2=expand(k2)
k2 =
-1/3*c^3*log(2)-1/3*c^3*log(c)-1/3*c^3*log(c+a)+C2+log(r)*C3
>> k2=subs(k2,'C2','1/3*c^3*log(2)+1/3*c^3*log(c)+C4')
k2 =
-1/3*c^3*log(2)-1/3*c^3*log(c)-1/3*c^3*log(c+a)+(+1/3*c^3*log(2)+1/3*c^3*log(c)+C4)+log(r)*C3
>> k2=simplify(k2)
k2 =
-1/3*c^3*log(c+a)+C4+log(r)*C3
>> p=k1+k2
p =
(4/9*c^2+1/9*r^2)*a-1/3*c^3*log(c+a)+C4+log(r)*C3
>> p=subs(p,'a','(r^2+c^2)^(1/2)')
p =
(4/9*c^2+1/9*r^2)*((r^2+c^2)^(1/2))-1/3*c^3*log(c+((r^2+c^2)^(1/2)))+C4+log(r)*C3
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