Your Wronskian w=e4x is correct. but what are W1 and W2? What equations do you get for the derivative of the "constants"?Cocoleia said:Homework Statement
y''-4y'+4y=(12e^2x)/(x^4)
I am trying to solve this differential equation. I know you would use the variation of parameters method, and I am trouble with the wronskian. My solution manual doesn't actually use a wronskian so I can't verify my work
Homework Equations
The Attempt at a Solution
I end up with w=e^4x
w1=(-12e^4x)/(x^3)
w2=(12e^4x)/(x^4)
But at this point the integrals for u1 and u2 seem rather impossible.
The Wronskian- variation of Params Problem is a mathematical concept used in differential equations. It involves solving for a set of parameters that satisfies a given differential equation and its boundary conditions.
The Wronskian- variation of Params Problem is commonly used in scientific research, particularly in fields such as physics, engineering, and economics. It is used to model and analyze various physical systems and phenomena, such as heat transfer, fluid dynamics, and population growth.
The key components of the Wronskian- variation of Params Problem include the differential equation, the boundary conditions, and the set of parameters being solved for. The Wronskian, a determinant formed from the solutions of the differential equation, is also an important component in solving this problem.
The difficulty of solving the Wronskian- variation of Params Problem depends on the complexity of the differential equation and the number of parameters being solved for. In some cases, it can be solved analytically, but in many cases, numerical methods must be used to approximate the solution.
Yes, the Wronskian- variation of Params Problem has many practical applications and can be used to model and solve real-world problems. It is commonly used in engineering and scientific research to analyze and understand various physical systems and phenomena.