variable seperable form using substitution method problem no 6

TL;DR

This video explains how to solve a problem based on the variable separable method using substitution.

Transcript

click the Bell icon to get latest videos from Ekeeda Hello friends in this video we are going to see one more problem which is based on variable separable method using substitution so let us start with problem number 6 so on Dy by DX is equal to Y by X a plus tan of Y by X here also we have a clear idea that the angle Y by X cannot be separated so ... Read More

Key Insights

• ❓ The variable separable method is a useful technique for solving differential equations.
• 👶 Substituting a new variable can sometimes simplify the equation and make it easier to solve.
• 🙃 Integrating both sides of the equation allows us to find the general solution.
• ❓ Logarithmic properties can be used to simplify the final solution.
• ❓ Practice and familiarity with the techniques are crucial for successfully solving such problems.
• 🎮 The video emphasizes the importance of understanding the steps and logic behind the solution.
• 🌍 The problem discussed showcases the application of the variable separable method in a real-world scenario.

Questions & Answers

Q: What is the problem being discussed in this video?

The problem being discussed in this video is how to solve the differential equation dy/dx = y/x + tan(y/x) using the variable separable method.

Q: How is the variable separable method applied to the problem?

The variable separable method is applied by substituting y/x as v, which allows the equation to be rewritten as v + x * dv/dx = v + tan(v).

Q: What is the solution to the problem?

The solution to the problem is love(sine(y/x)) = log(a) + log(b), where a and b are constants.

Q: Can you explain the steps involved in solving the problem?

The steps involved in solving the problem are: substituting y/x as v, separating the variables, integrating both sides, and simplifying the solution using logarithmic properties.

Summary & Key Takeaways

• The problem is to solve the differential equation dy/dx = y/x + tan(y/x) using the variable separable method.

• By substituting y/x as v, the equation can be rewritten as v + x * dv/dx = v + tan(v).

• We can separate the variables and integrate both sides, leading to the solution love(sine(y/x)) = log(a) + log(b).