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

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) Findthe general solution of thedifferential

A) Solve the following differentialequation by as many different methods as you can.
(See attachment forequation)
b) There is a type of differentialequation which will always be solvable by two different methods. What type of differentialequation is it and which other method can always be used to solve it?
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Please only do problems 3.62, 3.63, 3.68, 3.69, 3.71, 3.72, 3.74. PLEASE show all equations used, work and PLEASE do not skip steps no matter how minor. I learn by example and need to see everything also including pictures of current flow, directions, picture of how each step progressed, etc..
Please show pictures of step

Please work the problem and explain how you found the necessary values. Thank you.
Design a differential amplifier as shown in Figure 11.28 incorporating a basic two transistor current source to establish Iq. The bias voltages are V+=15V and V-=-15V, the transistor parameters are Beta=180 and Va=100V, and the maximum forwar

Findthe region in the xy plane in which theequation [(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.

An electric circuit with an ohmic resistor R and an inductance L will exhibit a certain delay in approaching the (asymptotic) saturation current I_infinity=U/R in response to a voltage source U. Using Kirchoff's circuit laws, electrical engineers have proposed theequation
dI/dt=-R/L I+U/L
for describing the time dependence I(

FIGURE 1 shows the electrostatic equivalent circuit of a human being. A person is charged to 20 kV and touches an object having a 50 Ω resistance to ground. Determine the following:
(a) the maximum current which will flow in the object
(b) the rise time of the current
(c) the decay time of the current
(d) the maximum volt

Linear Partial DifferentialEquation (II)
Non- Homogeneous Linear Partial DifferentialEquation with Constant Coefficients
Problem: Findthe solution of theequation (D2 - D'2 + D -