Differential Equations Answers

Form the difference equation generated by yx=a2x+b3x+c. (5 marks)

Find the constant a so that e^xy+y=x-1 is an implicit solution to dy/dx=(e^(-xy)+ay)/(e^(-xy)+x)

(D3 − 3DD′2 + 2D′3)z = 0

Verify that the equation

(23a - yz) dx + (2yz - xz) dy - (x 2- xy + y2) dz = 0

is integrable and find its integral. Only need integral

Find the integral curves of the equations

dx/(y+zx) = dy/-(x+yz) = dz/(x^2 - y^2)

Give the complete solutions of the twoo problems


1.7) Find a+b+c if phi (x) = a(e^x) + b(e^cx) is a solution to the initial value problem: second derivative of y + first derivative of y - 2y = 0; y(0) = 2, first derivative of y(0) = 1. Here a,b, and c are constants.


1.8) Find the positive constant a(>0) so that the parametric equation: x = at, y= -t^2 is a solution to y= x(dy/dx) + (dy/dx)^2.

Answer the questions and provide complete solution


1.5) Find the largest constant r so that phi(x) = e^rz is a solution to third derivative of y minus 2 times second derivative of y plus 2y = 0.


1.6) Find the smallest constant rso that phi(x) = x^r is a solution to (3)(x^2)(second derivative of y) + (11)(x)(first derivative of y) - 3y = 0, x > 0.

Answer the following and give complete solutions.


1. Find the constant a so that phi(x)=x(e^2x) is a solution to y'+ay-e^(2x)=0

2. Find the constant a so that e^xy + y = x-1 is an implicit solution to dy/dx = e^-xy +ay / e^-xy + x.

Find a general solution for the differential equation


(D^2 - 3D +2) = (e^2x)/(1+e^2x)

Charles' law states that, for an ideal gas at a constant pressure, — = k, where V (liters), T (degrees Kelvin) and k is a constant (lit/°K). What does this model tell us?