Page 1 of 1
An ODE y'= F(x, y) is called homogeneous of degree s if it is invariant with respect to the scaling (x, y) + (xx, Asy).
Posted: Tue Jul 12, 2022 12:45 pm
by answerhappygod
- An Ode Y F X Y Is Called Homogeneous Of Degree S If It Is Invariant With Respect To The Scaling X Y Xx Asy 1 (47.95 KiB) Viewed 31 times
An ODE y'= F(x, y) is called homogeneous of degree s if it is invariant with respect to the scaling (x, y) + (xx, Asy). This means that X-¹y = F(Xx, Xy), that is F(Xx, Xy) = X8-1F(x, y). A homogeneous ODE of degrees can be solved by adopting u(x): function. The function u will be invariant with respect to the scaling since u = (1) Find the general solution of the ODE and the solution for which y" + 4y' - 5y = 0 y(0) = 1, as well as the solution for which y(0) = 33, y'(0) = = 0 y (In 2) = 3. - y(x) Ta as new unknown X³y X.