- #1
Jonnyb42
- 186
- 0
[SOLVED] simple ODE problem, Bernoulli's Equation
Initial value problem:
Relation: t*y' - 2*[t^2]*sqrt(y) = 4*y
Initial value: y(1) = 4
general form of Bernoulli's equation:
y' + a(t)y = b(t)*[y^n]
First order, linear ODE form:
y' + a(t)y = b(t)
My written solution. I first get Bernoulli-type equation into first order/linear form. After that I solve it with the equation y = [1/mu]*Integral[ b(t) * mu dt] (+ constant)
where mu = e^[ Integral[ a(t) dt]
I have tried this multiple times and I get the same answer. When I plug in the solution y = f(t) it does not match the differential equation, (takes some time to show.)
Any help would be great, I obviously am doing something wrong.
Homework Statement
Initial value problem:
Relation: t*y' - 2*[t^2]*sqrt(y) = 4*y
Initial value: y(1) = 4
Homework Equations
general form of Bernoulli's equation:
y' + a(t)y = b(t)*[y^n]
First order, linear ODE form:
y' + a(t)y = b(t)
The Attempt at a Solution
My written solution. I first get Bernoulli-type equation into first order/linear form. After that I solve it with the equation y = [1/mu]*Integral[ b(t) * mu dt] (+ constant)
where mu = e^[ Integral[ a(t) dt]
I have tried this multiple times and I get the same answer. When I plug in the solution y = f(t) it does not match the differential equation, (takes some time to show.)
Any help would be great, I obviously am doing something wrong.
Last edited: