Differential equation solver plays an important role in science, Engineering and social sciences. Differential equation is mainly used in Mathematics and Science applications. Differential equation is an equation that involves a variable and its derivatives with respect to one or more independent variables. Differential equation is of two types, ordinary and partial. A differential equation is a differential equation in which a single independent variable enters explicitly or implicitly.
Problem 1: Solve the differential equation y d x – x d y = 0
Solution: Given equation is a separable equation so this can be written as d x / x = d y / y
=> Now integrate on both sides we get ln |x| + c = ln |y|
=> Taking exponent on both sides we get |y| = e^ c |x|
=> This can be written as |y| = C |x| C>0
=> The C in the second equation does not represent the same c in the first equation. This is general form of denoting constants.
=> Get rid of absolute value y = C x where c not equal to zero
=> The solution is y = C x.
Problem 2: Find the general solution of the equation xy^2 d x + (x – 1)(y+1) d y= 0
Solution: Given equation is separable equation xy^2 d x + (x – 1)(y+1) d y= 0
=> x d x / (x – 1) = - (y+1) d y / y^2
=> Now integrate on both sides we get x – ln |x – 1| + C = - ln |y| + (1/y)
=> This is general solution of the equation.