\r\n
\r\n Ordinary Differential Equation\r\n
\r\n
\r\n An ordinary differential equation (or simply ODE) is an equation of the form:\r\n $$y^{(n)}(x) = g(x)$$\r\n where \\(y^{(n)}(x)\\) is the \\(n^{th}\\) derivative of \\(y(x)\\) w.r.t. \\(x\\), i.e.,\r\n $$y^{(n)}(x) = \\frac{d^ny(x)}{dx^n}$$.\r\n
\r\n
\r\n -
First Order Ordinary Differential Equation
\r\n \n First order ordinary differential equation is a special form of ordinary differential equation that involve first order derivative. First order ordinary differential equations are\r\n also known as linear ordinary differential equations.\r\n $$y'(x) = g(x)$$\r\n
\r\n -
General Solution of a Linear Ordinary Differential Equation
\r\n \n The general solution of a linear ODE is given as:\r\n $$y(x) = \\int g(x) dx + c$$\r\n where \\(c\\) is the integration constant, and is determined by using boundary conditions.\r\n
\r\n -
Particular Solution of a Linear Ordinary Differential Equation
\r\n \n The general solution of a linear ODE is given as:\r\n $$y(x) = \\int g(x) dx + c$$\r\n Let's say the boundary condition is \\(y(x_0) = y_0\\).\r\n Using this boundary condition, we obtain the particular solution as:\r\n $$y(x) -y_0 = \\int g(x) dx $$\r\n
\r\n
\r\n
\n MagicGraph | Linear ODE\r\n
\r\n
In this MagicGraph, you will learn about solution of a linear ordinary differential equation and boundary condition.
\r\n
\r\n \r\n \r\n \r\n \r\n