dsolve gives wrong equations?

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daniel slama
daniel slama 2022 年 6 月 18 日
コメント済み: daniel slama 2022 年 6 月 19 日
hey all!
so i'm trying to learn how dsolve and I know i'm doing something incorrectly but i don't know exactly what.
it could just be that everything is in order but i am just bad at math lol.
anyway, examples are below/ would love some help.
>> syms y(x)
>> dsolve(diff(y)==y+sin(x))
ans =
C1*exp(x) - (2^(1/2)*cos(x - pi/4))/2 %should'nt the correct answer be -1/2*cos(t)-1/2*sin(t)+exp(t)*C1?
e.g 2:
syms y(x)
>> dsolve((diff(y))^2+y^2==1)
ans =
(exp(C1*1i - x*1i)*(exp(- C1*2i + x*2i) + 1))/2 %shoud'nt these two be sin(s-C1) and -sin(s-C1)?
(exp(C2*1i + x*1i)*(exp(- C2*2i - x*2i) + 1))/2
1 %legit
-1 %legit

採用された回答

Torsten
Torsten 2022 年 6 月 18 日
編集済み: Torsten 2022 年 6 月 18 日
There are often several ways to write a function. But it seems to me that your S2 solutions are not independent.
syms y(x) C1
S1 = dsolve(diff(y)==y+sin(x))
S1 = 
S2 = -1/2*cos(x)-1/2*sin(x)+exp(x)*C1
S2 = 
res1 = simplify(diff(S1,x)-S1-sin(x))
res1 = 
0
res2 = simplify(diff(S2,x)-S2-sin(x))
res2 = 
0
S1 = dsolve((diff(y))^2+y^2==1)
S1 = 
S2 = [sin(x-C1) ;-sin(x-C1)]
S2 = 
res1 = simplify(diff(S1,x).^2+S1.^2-1)
res1 = 
res2 = simplify(diff(S2,x).^2+S2.^2-1)
res2 = 
  1 件のコメント
daniel slama
daniel slama 2022 年 6 月 19 日
damn, TYSM.
i never would have figured this out on my own

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