Learn with engr.ayesha

https://youtu.be/TO-NgkbKnj0
In this video we will discuss about rules of replacement or logical equivalance rules. How these rules are different from rules of inferences or validity rules.we will also solve some question by applying these rules.

solve this example using variation of parameter method
y"-4y = e²ˣ/x
https://youtu.be/24uMEd0rtvc

General solution of non homogeneous differential equation by Undetermined coefficient method plus one solved example.
https://youtu.be/wRUjhuh-jjc

Lec 2: validity rule / rules of inference in detail with some solved question

https://youtu.be/XpjcZGM1fDY

Lect 1: basic concept of logic and critical thinking.
https://youtu.be/NnG4iI0dBEY

In this lecture we will discuss how to find the general solution of non homogeneous differential equation or 2nd order linear D.E by using variation of parameter method.
we will also differentiate variation of parameter method with undetermined coefficient method. Here we will solve one example by using variation of parameters method for finding solution.

Example : y"+y=secx variation of parameter method.

By finding complementary solution and particular solution we will find out the solution of non homogeneous differential equation which will be equal to the sum of complementary solution and particular solution.

so y = yc + yp

Variation of parameters method: in this method we replace the constant of complementary solution with arbitrary functions. we will find these function using wronskian method.

video link for finding solution of non homogeneous D.E using undetermined coefficient method.

https://youtu.be/wRUjhuh-jjc