- #1
Icebreaker
How do I go about solving
x^2y' - cos (2y) = 1
This is unlike anything I've seen so far. Or so I think.
x^2y' - cos (2y) = 1
This is unlike anything I've seen so far. Or so I think.
Last edited by a moderator:
Icebreaker said:How do I go about solving
x^2y' + cos (2y) = 1
This is unlike anything I've seen so far. Or so I think.
Yessaltydog said:It's separable right?
Icebreaker said:18 down, 2 more to go:
y' = (4x + 2y - 1)^(1/2)
and
(1-xy)y' + y ^2 + 3xy^3 = 0
The last one kinda looks like Riccati, but I can't get it to work.
edit: I got the second one. One more ODE remains... I don't know how to approach that one.
The equation "Dif Eq x^2y' - cos(2y) = 1" is used to model and solve problems involving exponential growth or decay, such as population growth, radioactive decay, and economic growth.
In this equation, x represents the independent variable, y represents the dependent variable, and y' represents the derivative of y with respect to x.
The general solution to this equation is y(x) = ±√(C + x^2 + sin(2y)), where C is a constant of integration.
Yes, this equation can be solved analytically using various methods such as separation of variables, integrating factor, or substitution.
This equation can be applied to study and predict growth or decay in various fields such as biology, chemistry, physics, and economics. It can also be used to model oscillations and periodic phenomena.