Differential Equations Answers

Solve the differential equation
dy/dx + (x/1-x^2)y=xy^1/2, y(0)=1

The function f(x,y) = max {y/x,x} is a homogeneous function on R^2

P(x)y"+a(x)y'=0

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.