Yahoo Answers is shutting down on May 4th, 2021 (Eastern Time) and the Yahoo Answers website is now in read-only mode. There will be no changes to other Yahoo properties or services, or your Yahoo account. You can find more information about the Yahoo Answers shutdown and how to download your data on this help page.
Trending News
Solve the initial value problem y"+16y=0, y(0)=1, y'(0)=0?
This was on the exam today, had no idea how to approach this since i'm so accustomed to solving Eigen values of decoupled systems. And in the heat of the moment couldn't see any relationships.
A) Find the Eigen values
B) Find associated Eigen vectors
C) Find gen Sol
D) Solve initial values
2 Answers
- GlippLv 77 years agoFavorite Answer
suppose y = Ae^(λx)
then y'' + 16y = (Aλ² + 16A)e^(λx)
=> λ² + 16 = 0
=> λ = ±4i
=> y = A₁e^(4ix) + A₂e^(-4ix)
=> y = B₁cos(4x) + B₂sin(4x)
y(0) = 1 => B₁ = 1
y'(0) = 0 => B₂ = 0
y = cos(4x)
- ramuLv 57 years ago
y"+16y=0
d^2y/dx^2+16y=0
integration of it
y'+16yx+c=0-->y'=-16yx-c
integration of it again
y+16yx^2+cx+d=0-->y=(-cx-d)/(1+16x^2)
y'(0)=0 that means 0=0-c so c=0
y(0)=1 that means 1=(0-d)/(1+0) that means d=-1
so final eq y+16yx^2-1=0
y+16yx^2=1
y=1/(1+16x^2)
