Solve the equation

Find the solution to: (6xy-y^3)dx + (4y+3x^2-3xy^2)dy =0

Solve the equation

(2xy)dx + (y^2-3x^2)dy = 0

Pursuit Problem

A dog walks north from a crossroads at 1 mile per hour. The dog's master begins one mile east of the crossroads and walks AT ALL TIMES directly at the dog with a speed of s>1 miles per hour. 1. Find the equation (in the form y = f(x)) that describes the path of the master. 2. When and where does the master overtake the dog if s=1.5? 3. Find the function that gives the meeting time in terms of s.

laplace transform

use the laplace transform to solve the ODE y"+3y = cos(2t), y(0)=0 , y'(0)=0 show all details related to using the inverse transform

convolution

use the definition of convolution to show that f*g=g*f