(a) A simple model for the shape of a tsunami is given by dw = w4 - 2W, dx where W(x) > O is the height of the wave expressed as a function of its position relative to a point offshore. By inspection, find all constant solutions of the DE. (Enter your answers as a comma-separated list.) W = (b) Solve the differential equation in part (a). A CAS may be useful for integration. (Use C for the constant of integration.) W(x) = (c) Use a graphing utility to obtain the graphs of all solutions that satisfy the initial condition w(0) = 2. w

Q: 4. Find a general solution of the differential equation z"-3x + 2x=c² sin

A:

Q: Find the differential of the function. y = e³x dy = =

A: We have given function  y=e3x dydx=ddxe3x dydx=e3x·ddx3x dydx=e3x·3 dydx=3e3x dy=3e3x dx

Q: . Write the equation of the line parallel to y = 6X - 1 that passes through the point (-2,1) in…

A:

Q: Form the differential equation for the function y = acos(2x + b)

A: By finding first and second derivatives of function we form the required differential equation as…

Q: (3x* – 1)y=x- Zx° †X 2. Find the differential equation of all straight lines at 2- unit distance…

A:

Q: Solve the differential equation dr dr 6-+9x=0; when t=0, x=2 and =0. dr dr2 dr

A: The given differential equation is                             d2xdt2-6dxdt+9x=0  with         when…

Q: The rate of increase in a bank account is 4% of the amount in the account; the initial deposit is…

A: Note: There are multiple sub questions. No specific question has been asked. So, We will solve the…

Q: Differentiate the implicit equation with respect to x. x³ + y³ ln(x) + e²y = 5

A:

Q: Solve the exact differential equation (x* + y)dx +(3xy +1)dy = 0

A:

Q: find the homogenous linear equation of the function y = x2 sinx+ e5x

A:

Q: An object weighting 16 pounds is attached to a string, thereby stretching the spring 12 inches. The…

A:

Q: Prove that if -1 <r<1, then 100 n=1 mon

A: To prove that if -1&lt;r&lt;1, then                             ∑n=1∞rn    converges and has a sum…

Q: ind the differential equation of all parabolas whose axis are parallel to the x-axis and have latus…

A: Since equation of parabola whose axis is parallel to the x-axis and have latus rectum a is…

Q: V34

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.