Problem solving a separable differential equation for u

[mesa]

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]

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?

Hint: Use the laws of exponents to split e^{5u + 2t}.

 

[mesa]

Hint: Use the laws of exponents to split e^{5u + 2t}.

Damn it...

Thank you, its been a long night.