How do you solve a linear second order differential equation?
To solve a linear second order differential equation of the form . d 2 ydx 2 + p dydx + qy = 0. where p and q are constants, we must find the roots of the characteristic equation. r 2 + pr + q = 0. There are three cases, depending on the discriminant p 2 – 4q. When it is . positive we get two real roots, and the solution is. y = Ae r 1 x + Be r 2 x
What is the general solution of the differential equation?
So the general solution of our differential equation is: y = Ae (2 3x) + Be (−3 2x) Example 4: Solve 9 d2y dx2 − 6 dy dx − y = 0
How do you solve the differential equation p2 – 4q?
How we solve it depends which type! We can easily find which type by calculating the discriminant p2 − 4q. When it is When the discriminant p2 − 4q is positive we can go straight from the differential equation y = Ae (2 3x) + Be (−3 2x)
What are the derivatives of d2y dx2?
First take derivatives: d2y dx2 = 4Ae 2x + 9Be −3x (4Ae 2x + 9Be −3x) + (2Ae 2x − 3Be −3x) − 6 (Ae 2x + Be −3x) = 0
What is the Order of the derivative of the differential equation?
Differential Equations are classified on the basis of the order. Order of a differential equation is the order of the highest order derivative (also known as differential coefficient) present in the equation. In this equation the order of the highest derivative is 3 hence this is a third order differential equation.
What is the degree of the differential equation?
So, the degree of the differential equation is 1 and it is a first order differential equation. Note: If the DE in which differential coefficient is present inside the parenthesis of any another function as a composite, then first attempt to make it as simple as possible.
What is the Order of P and Q in this equation?
P and Q are either constants or functions of the independent variable only. This represents a linear differential equation whose order is 1. This also represents a First order Differential Equation. When the order of the highest derivative present is 2, then it is a second order differential equation.