Скачать с ютуб 🔵19 - Fundamental Sets of Solution and Wronskian, Principle of Superposition of Differential Equ's в хорошем качестве

🔵19 - Fundamental Sets of Solution and Wronskian, Principle of Superposition of Differential Equ's

So still considering a second order linear homogeneous diff equation is given of the form p(x)d^2y/dx^2 + q(x)dy/dx +r(x)y = 0, where p, q and r are all functions of x. Let y1 and y2 be two linearly independent solutions of a differential equation and c1 and c2 be constants. then, the general solution to the differential equation is given by: y = c1y1 + c2y2, We can do same using wronskian, i.e, 1. if the wronskian is not equal to zero, the two functions are linearly independent. The two functions form the fundamental sets of solutions. 2. if the two functions are linearly dependent, their wronskian is zero. Notice that, it is wrong to say if the wronskian is zero, the two functions are linearly dependent. Wronskian = det of a matrix. 00:00 - Fundamental Sets of Solution 01:05 - Linearly Dependence and Independence 12:59 - Fundamental Sets of Solution 03:28 - Principle of Superposition 07:20 - Wronskian 10:12 - General Solution by Wronskian 13:39 - Example 1 Playlists on various Course 1. Applied Electricity    • APPLIED ELECTRICITY   2. Linear Algebra / Math 151    • LINEAR ALGEBRA   3. Basic Mechanics    • BASIC MECHANICS / STATICS   4. Calculus with Analysis / Calculus 1 / Math 152    • CALCULUS WITH ANALYSIS / CALCULUS 1 /...   5. Differential Equations / Math 251    • DIFFERENTIAL EQUATIONS   6. Electric Circuit Theory / Circuit Design    • ELECTRIC CIRCUIT THEORY / CIRCUIT DESIGN   Make sure to watch till the end. Like, share, and subscribe. Thank you.