mesa said:Homework Statement
Solve the separable differential equation for u
du/dt=e^(5u+2t)
Use the following initial condition: u(0)=13
The Attempt at a Solution
Honestly I didn't get very far on this one. I took the natural log of both sides,
ln du/dt = 5u+2t
And now I am stuck. Should I divide both sides first by our e^(5u+2t) instead of taking the ln?
Mark44 said:Hint: Use the laws of exponents to split e5u + 2t.
A separable differential equation is a type of differential equation where the variables can be separated into two functions that can be integrated separately. This allows for a simpler solution to the equation.
To solve a separable differential equation, you must first separate the variables into two functions. Then, you can integrate both sides of the equation separately. This will give you a general solution, which can be further simplified by applying initial conditions.
The steps involved in solving a separable differential equation are:
Solving separable differential equations is useful in many areas of science, engineering, and economics. It can be used to model population growth, radioactive decay, chemical reactions, and many other phenomena.
The main challenge of solving a separable differential equation is identifying the correct method to separate the variables and finding a solution that satisfies any given initial conditions. This can be difficult for more complex equations and may require advanced mathematical techniques.