# Differential Equation Solver

## Online Tutoring Is The Easiest, Most Cost-Effective Way For Students To Get The Help They Need Whenever They Need It.

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.