method of variables separable problem no 10

TL;DR

Learn how to solve a variable separable method problem by finding the principal solution in this video.

Transcript

click the bell icon to get latest videos from equator hello friends in this video we are going to see last problem which is based on variable separable method let us start with problem number 10 solve DX by DT is equal to 6 minus 3 X if X is equal to 0 when T is equal to 0 in this question they asked you to find the principal solution as the values... Read More

Key Insights

• ❓ The problem involves solving a differential equation using the variable separable method.
• ❓ The general solution is obtained by integrating the equation.
• 😀 The constant C is determined by substituting given values.
• 😀 The principal solution is obtained by substituting the value of C into the general solution.
• 💁 Variable separable form simplifies the integration process.
• ❓ The solution involves logarithmic functions.
• 🎮 The video emphasizes finding the principal solution by following a step-by-step process.

Questions & Answers

Q: What is the first step in solving the variable separable method problem?

The first step is to find the general solution by integrating DX/DT = 6 - 3X on both sides of the equation.

Q: How is the constant C determined in the problem?

The constant C is found by substituting the given values of X and T (0 and 0) into the general solution and solving for C.

Q: How is the principal solution obtained?

The principal solution is obtained by substituting the value of C into the general solution and simplifying the expression.

Q: What is the importance of variable separable form in solving this problem?

By converting the equation into variable separable form, the integration process becomes easier and allows for separate integration of the variables.

Summary & Key Takeaways

• The video discusses problem number 10 involving solving the equation DX/DT = 6 - 3X using the variable separable method.

• To find the principal solution, the general solution is first determined by integrating both sides of the equation.

• By substituting the given values of X and T into the general solution, the constant C is found and used to obtain the final principal solution.