Differential Equation (IX): Formation of DifferentialEquations by Elimination
Eliminate the arbitrary constants from the equation: y = Ae^x + Be^2x + Ce^3x. Make sure to show all of the steps which are involved.

Question 1.
1) Find a vector normal to the surface z + 2xy = x2 + y2 at the point (1,1,0).
2) Determine if there are separable differentialequations among the following ones and explain:
a) dy/dx=sin(xy),
b) dy/dx = (xy)/(X+y)
c) dr/d(theta) = (r^2+1)cos(theta)
3) Find the general solution of the differential

For each of the following ordinairy differentialequations, indicate its order, whether it is linear or nonlinear, and whether it is autonomous or non-autonomous.
a) df/dx +f^2=0
(See attachment for all questions)

A) Solve the following differential equation by as many different methods as you can.
(See attachment for equation)
b) There is a type of differential equation which will always be solvable by two different methods. What type of differential equation is it and which other method can always be used to solve it?
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Find the region in the xy plane in which the equation [(x - y)^2 - 1] u_xx + 2u_xy + [(x - y)^2 - 1] u_yy = 0 is hyperbolic. The complete problem is in the attached file.

1. Please see the attached file for the fully formatted problems.
a) Use separation of variables to solve
b) Solve the following exact differential equation
c) By means of substitution y=vx solve the differential equation
d) By means of the substitution for approipriate values of and , solve the d

Hi,
Please help working on
section 1.1 problems 2,4,8,14,16
section 1.2 problems 6,10,20,24,27
thank you
See attached
Classify each as an ordinary differential equation (ODE) or a partial differential equation (PDE), give the order, and indicate the independent and dependent variables. If the equation is an ODE, ind

1. Complex Exponentials: Simply the following expression and give your answer both in polar and rectangular form.
o c=3ejπ/4+4e−jπ/2
2. Difference Equations: Solve the following difference equation using recursion by hand (for n=0 to n=4)
o y[n] + 0.5y[n-1] = 2x[n-1]; x[n] = δ[n], y[-1] = 0
3. DifferentialEquations