Brij Mohan | Differential Equations

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Plotting of Legendre Polynomial for n=1 to n=5 in the interval [0,1], verifying graphically that all roots of Pn(x) lie in the interval [0,1].

For n=1

For n=1

For n=2

For n=2

For n=3

For n=3

For n=4

For n=4

For n=5

For n=5

Automatic computation of coefficients in the series solution near ordinary point.

OR

Finding Power Series solution of differential equation near ordinary point.

Example 1 with Solution

Example 1 with Solution

Program

Program

Output

Output

Example 2(IVP) & Solution

Example 2(IVP) & Solution

Example 2..Continue

Example 2..Continue

Program

Program

Output

Output

Plotting of the Bessel's function of first kind of order 0 to 3.

Order - 0

Order - 0

Order - 1

Order - 1

Order - 2

Order - 2

Order - 3

Order - 3

Automating the Frobenious series method near regular singular point.

Example

Example

Example continue

Example continue

Program

Program

Output

Output

Output continue

Output continue

Use of Laplace transforms to plot the solution of Mass-Spring System with and without external forces.

Use of Laplace transforms to plot the solution of LCR circuits with applied voltage. Plotting of current and charge w.r.t. time.

With External Forces

With External Forces

Without External Forces 1

Without External Forces 1

Without External Forces 2

Without External Forces 2

Example 1

Example 1

Underdamped Series Circuit

Example 2

Example 2

Underdamped Series Circuit

Example 3

Example 3

Overdamped Series Circuit

Example 4

Example 4

Critically Damped Series Circuit

Example 5

Example 5

Underdamped Series Circuit

Example 6

Example 6

Underdamped Series Circuit

Finding and ploting Laplace transforms of various functions and solving differential equations using Laplace transform.

Finding and Ploting of Laplace Transform

Finding and Ploting of Laplace Transform

Solving Differential Equations using Laplace Transform

Solving Differential Equations using Laplace Transform

Solving Boundry Value Problems

Boundry Value Problem 1

Boundry Value Problem 1

Boundry Value Problem 2

Boundry Value Problem 2

Finding Fourier series and ploting for order n=1 to 6

Example 1

Example 1

Example 2

Example 2

Example 3

Example 3

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