Solve the IVP. Check that your answer satisfies the ODE as well as the initial conditions. Show the details of your work. y''+y'-6y=0, y(0)=10, y'(0)=0

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

Solve the given initial-value problem.

$$y ^ { \prime \prime } + 16 y=0, y(0)=2,y'(0)=-2$$

Given that $m^4+6m^3+11m^2+6m+1=(m^2+3m+1)^2$ find the general solution of $y^{iv}+6y'''+11y''+6y'+y=0$

Solve the differential equation.

$$y’’-y’-6y=0$$

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

Find a general solution to the given differential equation. \

$$9y'' - 30y' + 25y = 0$$

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

Find the motion of the mass–spring system modeled by the ODE and the initial conditions. Sketch or graph the solution curve. In addition, sketch or graph the curve of y-yp to see when the system practically reaches the steady state. Solve y''+25y=99 cos 4.9t, y(0)=2, y'(0)=0. How does the graph of the solution change if you change (a) y(0), (b) the frequency of the driving force?

Solve the problem, showing the details of your work. Sketch or graph the solution. (x²D²+15xD+49l)y=0, y(1)=2, y'(1)=-11

Find a general solution to the given differential equation. \

$$9y'' - 30y' + 25y = 0$$

Solve the problem, showing the details of your work. Sketch or graph the solution. (x²D²+xD-l)y=16x³, y(1)=-1, y'(1)=1

Extend the method to products of the function (b) Extend the method to Euler-Cauchy equations. Comment on the practical significance of such extensions.

Solve the problem, showing the details of your work. Sketch or graph the solution. y''-3y'+2y=10sinx, y(0)=1, y'(0)=-6