Differential equations solver is a tool used to solve the differential equations which contains variables and their derivatives. Apart from this it also solves different order differential equation such as first order, second order etc. They are of ordinary or partial derivative. In simple words we can say that differential equations are equations that contain derivative of functions or differentials.
Problem 1: Solve the differential equation d y / d x = 1 + x + y + x y
Solution: Given equation is written as d y / d x = (1 + x) + y (1 + x)
=> d y / d x = (1 + x) (1 + y)
=> d y / (1 + y) = (1 + x) d x
=> Integrating we have, log (1 + y) = x + (x^2/2) + c which is required solution.
Problem 2: Solve 3 ex tan y d x + (1 + ex) sec2 y d y = 0
Solution: The given equation can be written in the form of 3 ex / (1 + ex) d x = ( sec2 y / tan y )d y
=> Integrating on both sides we get, 3 log (1 + ex) + log tan y = log c
=> Taking log outside we get, log ( tan y (1 + ex) ^3) = log c
=> Now we can cancel log on both sides
=> tan y (1 + ex) ^3 = c.
=> Therefore, the required solution is (1 + ex) ^3 tan y = c