Help with part e please M Drafts 1 mauradperez xUntitled 0

Help with part (e), please!

M Drafts (1) - mauradperez xUntitled ×0 MAURA PEREZ-Outloo, × \\ G Find the general solutio \\ e Chegg Study | Guided Sc × www.math.utah.edu/~korevaar/2250fall16/hw9.pdf Untitled 2/4 Hint: Find a root r, of the cubic characteristic polynomial, then divide it by (r - r, ) to get a quotient quadratic polynomial b) Find the general solution to the differential equation for x(t) Hint: completing the square works well here - probably better than the quadratic formula. Solve the initial value problem for the differential equation inh, with x(0) 0, x, (O) 10 d) Find the general solution to the differential equation for y(x) Find the general solution to the differential equation for y(x) 12:00 PM 4x 10/27/2016

Solution

e)

linear homogeneous equation with constant coefficients

SO soluiton is of the form: y=exp(kx)

Substituing gives

k^5+6k^3+9k=0

k(k^4+6k^2+9)=0

k=0,k^4+6k^2+9=0

k=0, (k^2+3)^2=0

k=0,k^2=-3

k=0,k=i sqrt{3},-i sqrt{3}

Both the complex roots are repeated roots

So general solution is

y(x)=A+((Cx+E) sin(sqrt{3}x)+(Dx+F) cos(sqrt{3}x))