Why is dsolve giving me the wrong answer?

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Crystal Judd Unson
Crystal Judd Unson on 5 Oct 2021
Commented: Star Strider on 31 Oct 2021
Hi, I'm trying to solve a 4th order differential equation using dsolve but I got a wrong answer. This is my script:
syms y(x)
Dy(x)=diff(y);
D4y(x)=diff(y,4);
y4=dsolve('D4y+8*D2y+16*y==0')
When I executed it I got the following,
y4=C1*cos(2*t) - C3*sin(2*t) + C2*t*cos(2*t) - C4*t*sin(2*t)
The answer should be y4=C1*cos(2*t) + C3*sin(2*t) + C2*t*cos(2*t) + C4*t*sin(2*t). What went wrong in my code? Thank you!
  1 Comment
Star Strider
Star Strider on 31 Oct 2021
syms y(x)
syms C1 C2 C3 C4 positive
Dy(x)=diff(y);
D2y = diff(y,2);
D3y = diff(y,3);
D4y(x) = diff(y,4);
ic = [y(0)==C1, Dy(0)==C2, D2y(0)==C3, D3y(0)==C4];
y4 = dsolve(D4y+8*D2y+16*y==0, ic)
y4 = 
.

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Answers (1)

Kumar Pallav
Kumar Pallav on 31 Oct 2021
Hi,
As per my understanding, C1, C2,C3,C4 are arbitrary constants(can be positive or negative) and hence, the answer you got and the expected answer is not different.

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