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🔵22 - Method of Variation of Parameters 1 - Non-Homogeneous Differential Equations
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In this lesson we shall learn how to solve the general solution of a 2nd order linear non-homgeneous differential equation using the method of variation of parameters.
Given a non-homogeneous differential equation: ay'' + by' + cy = G(x), where G(x) is not zero.
The general solution is given by: y = yc + yp.
To find the general solution, you first need to treat the given D.E as a homogeneous D.E, and solve its general solution - that becomes the general solution called the complementary function, yc.
For the yp, the particular integral, is obtained using the method of variation of parameter.
yp = u1y1 + u2y2.
With that we vary the parameters, by replacing c1 and c2 with two unknown functions of x.
To find u1 and u2, we first need to find the wronskian of the two functions.
00:00 - Introduction
04:15 - Ex 1
Playlists on various Course
1. Applied Electricity
2. Linear Algebra / Math 151
3. Basic Mechanics
4. Calculus with Analysis / Calculus 1 / Math 152
5. Differential Equations / Math 251
6. Electric Circuit Theory / Circuit Design
Make sure to watch till the end.
Like, share, and subscribe.
Thank you.
Given a non-homogeneous differential equation: ay'' + by' + cy = G(x), where G(x) is not zero.
The general solution is given by: y = yc + yp.
To find the general solution, you first need to treat the given D.E as a homogeneous D.E, and solve its general solution - that becomes the general solution called the complementary function, yc.
For the yp, the particular integral, is obtained using the method of variation of parameter.
yp = u1y1 + u2y2.
With that we vary the parameters, by replacing c1 and c2 with two unknown functions of x.
To find u1 and u2, we first need to find the wronskian of the two functions.
00:00 - Introduction
04:15 - Ex 1
Playlists on various Course
1. Applied Electricity
2. Linear Algebra / Math 151
3. Basic Mechanics
4. Calculus with Analysis / Calculus 1 / Math 152
5. Differential Equations / Math 251
6. Electric Circuit Theory / Circuit Design
Make sure to watch till the end.
Like, share, and subscribe.
Thank you.
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