Solve Bernoulli Equation x'=b(t)x+c(t)x^n when n<0

The|M|onster
Messages
83
Reaction score
0
How do I solve a Bernoulli equation of the form x' = b(t)x + c(t)x^n when n < 0?
 
Physics news on Phys.org
The|M|onster said:
How do I solve a Bernoulli equation of the form x' = b(t)x + c(t)x^n when n < 0?


\frac{dx}{dt}-b(t)x=c(t)x^{n} A standard substitution is v=x^{1-n}
 
Thank you very much. it worked perfectly.
 
Thread 'Direction Fields and Isoclines'

Thread 'Direction Fields and Isoclines'

I sketched the isoclines for $$ m=-1,0,1,2 $$. Since both $$ \frac{dy}{dx} $$ and $$ D_{y} \frac{dy}{dx} $$ are continuous on the square region R defined by $$ -4\leq x \leq 4, -4 \leq y \leq 4 $$ the existence and uniqueness theorem guarantees that if we pick a point in the interior that lies on an isocline there will be a unique differentiable function (solution) passing through that point. I understand that a solution exists but I unsure how to actually sketch it. For example, consider a...
View full post »

Similar threads

MHB Help with a question (Bernoulli General solution)
Replies
8
Views
2K
A Solving for a steady-state (passive cable equation)
Replies
4
Views
2K
A Differential equation and Appell polynomials
Replies
1
Views
3K
I On vibrating string and differentiating infinite sum
Replies
7
Views
3K
I On error estimates of approximate solutions
Replies
1
Views
3K
Is This ODE a Bernoulli Equation and Can It Be Solved with Substitution?
Replies
3
Views
2K
I Fundamental matrix of a second order 2x2 system of ODEs
Replies
2
Views
4K
I On the approximate solution obtained through Euler's method
Replies
1
Views
3K
MHB Solving the Wave Equation with Nonzero Initial Velocity
Replies
2
Views
2K
A Show positivity and boundedness of a non-linear system
Replies
2
Views
493

Hot Threads

Recent Insights

Back
Top