Solve the IVP. Check that your answer satisfies the ODE as well as the initial conditions. Show the details of your work. 9y''-30y'+25y=0, y(0)=3.3, y'(0)=10.0

Solve the IVP. Check that your answer satisfies the ODE as well as the initial conditions. Show the details of your work. y''-k²y=0(k≠0), y(0)=1, y'(0)=1

(a) Verify that $y$ is a solution of the ODE.

(b) Determine from y the particular solution of the IVP.

(c) Graph the solution of the IVP.

$$y'+4y=1.4$$

$$y=ce^{-4x}+0.35$$

$$y(0)=2$$

Find the final discount date and the net payment date.

Calculate the value of the multiple integral.

$\iiint_T x y d V$, where $T$ is the solid tetrahedron with vertices $(0,0,0),\left(\frac{1}{3}, 0,0\right),(0,1,0)$, and $(0,0,1)$

(a) Verify that the given functions are linearly independent and form a basis of solutions of the given ODE. (b) Solve the IVP. Graph or sketch the solution.

Find a general solution. Check your answer by substitution. 10y''-32y'+25.6y=0

Solve the following ODEs, showing the details of your work. y'''+3y''+3y'+y=e^x-x-1

Find a general solution. Check your answer by substitution. y''+9y'+20y=0

Solve the IVP. Check that your answer satisfies the ODE as well as the initial conditions. Show the details of your work. 8y''-2y'-y=0, y(0)=-0.2, y'(0)=-0.325

Solve the IVP. Check that your answer satisfies the ODE as well as the initial conditions. Show the details of your work. y''-y=0, y(0)=2, y'(0)=-2

Solve the IVP. Check that your answer satisfies the ODE as well as the initial conditions. Show the details of your work. 4y''-4y'-3y=0, y(-2)=e, y'(-2)=-e/2

y''+ay;+by=0 for the given basis.

$$e^{-3.1x}cos 2.1x\text{, }e^{-3.1x}sin2.1x$$

y''+ay'+by=0 for the given basis. cos 2πx, sin 2πx.