Solution of Higher Order Differential Equation when R.H.S = X.V

TL;DR

Learn how to solve higher order differential equations with the right-hand side as x into some function of x.

Transcript

hello students so now we are going to start with the new method in which we will see how to solve the given higher order differential equation when your right hand side is x into some function of x it means x into v now guys if we have right hand side as x into v where b is a function of x there are set of rules which we have to follow to get the a... Read More

Key Insights

• ✋ To solve higher order differential equations, it is important to follow two steps: finding the complementary function and the particular integral.
• 💁 The complementary function is obtained by converting the differential equation into the form of the operator d and solving the auxiliary equation.
• 😄 The particular integral can be found using a formula that involves applying the function of d on the given function of x.
• 🪜 The final solution is obtained by adding the complementary function and particular integral.
• 👉 This method can be used for higher order differential equations with the right-hand side as x into some function of x.
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Questions & Answers

Q: What are the steps to solve a higher order differential equation with x into v as the right-hand side?

The steps are to find the complementary function by converting the equation into the form of the operator d and solving the auxiliary equation, and then find the particular integral using a formula that involves applying the function of d on the given function of x.

Q: How do you find the complementary function?

To find the complementary function, convert the differential equation into the form of the operator d and equate it to zero. Solve the auxiliary equation to get the roots and use them to obtain the complementary function.

Q: What is the formula for finding the particular integral?

The formula for finding the particular integral when the right-hand side is x into v is 1/(function of d) * x * (x - f' of d)/(function of d), where f' of d is the derivative of the given function of x with respect to d.

Q: How do you combine the complementary function and particular integral to get the final solution?

Add the complementary function and particular integral together to obtain the final solution of the higher order differential equation with x into some function of x as the right-hand side.

Summary & Key Takeaways

• The video discusses two steps to solve higher order differential equations with the right-hand side as x into some function of x.

• Step 1: Find the complementary function by converting the differential equation into the form of the operator d and solving the auxiliary equation.

• Step 2: Find the particular integral using a formula that involves applying the function of d on the given function of x.