Exercise
$\frac{dn}{dt}+n=nte^{t+5}$
Step-by-step Solution
Learn how to solve problems step by step online. Solve the differential equation dn/dt+n=nte^(t+5). Grouping the terms of the differential equation. Factor the polynomial nte^{\left(t+5\right)}-n by it's greatest common factor (GCF): n. Group the terms of the differential equation. Move the terms of the n variable to the left side, and the terms of the t variable to the right side of the equality. Integrate both sides of the differential equation, the left side with respect to n, and the right side with respect to t.
Solve the differential equation dn/dt+n=nte^(t+5)
Final answer to the exercise
$\ln\left|n\right|=e^{\left(t+5\right)}t-e^{\left(t+5\right)}-t+C_0$