Which of the following is not a solution

Anahi Solomon

Anahi Solomon

Answered question


Which of the following is not a solution of y+4y=0
(A) 4cos(2x)
(B) 5sin(2x)
(C) sin(2x)cos(2x)
(D) 4cos(2x)+5sin(2x)

Answer & Explanation



Beginner2022-03-23Added 13 answers

The given equation is a second order linear non homogeneous differential equation with constant coefficient.
The general solution for a(x)y+b(x)y+c(x)y=g(x)
The general solution of the given differential equation can be written as
yh is the solution to the homogeneous ODE a(x)y+b(x)y+c(x)y=0
Here the given ODE is the homogeneous equation.
The complementary solution for the given equation is:
Rewrite the equation with y=eγx
γ2+4=0 γ=2i, γ=2i
For two complex roots γ1qγ2, where γ1=a+ib, γ2=aib
the general solution takes the form: y=eax(c1cos(bx)+c2sin(bx))
Now, there are four options and one option is incorrect:
(A) 4cos(2x) is possible when c1=4 and c2=0
(B) 5sin(2x) is possible when c1=0 and c2=5
(C) sin2xcos(2x) is not possible
(D) 4cos(2x)+5sin(2x) is possible when c1=4 and c2=5
Hence the solution (C) is not possible
Jeffrey Jordon

Jeffrey Jordon

Expert2022-03-31Added 2605 answers

Answer is given below (on video)

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