Any problem in this then comment below. I will help you.
Answer = (-7,7)
Here this problem not defined on p=7 and p=-7 ..
So these two points divide this into 3 interval...
(-inf,-7) , (-7,7) ,(7,inf) ..
Now initial condition is on p=-6 . That lies in 2nd interval..
So unique solution defined in (-7,7) ..
(1 point) The IVP 8(-6) = 1029 d.-4 has a unique solution defined on the interval
The IVP sin(t)d2xdt2+cos(t)dxdt+sin(t)x=tan(t) x(1)=17 dxdt∣∣1=8 has a unique solution defined on the interval
9. (4 points) Does there exist a unique solution to the following IVP in a neighborhood of the initial condition? Find all constant solutions, if any. Specify the largest interval over which your constant solution is valid. Justify your answers. dy (ey-)(tan y) In(1 -),y(0)-3/2
9. (4 points) Does there exist a unique solution to the following IVP in a neighborhood of the initial condition? Find all constant solutions, if any. Specify the largest interval over which your constant solution...
For the following linear, second-order IVP, find the largest interval on which a unique solution is guaranteed to exist. +2-1 y" + +12y + cos(t) (t+2) sin(t) Y = y(2) = 11, y(2) = 4 t+1)
Please Solve the IVP and define the interval at which the solution
is defined. Please show steps clearly
di dt 29, L-+ Ri = E, ㈣ = , L, R, E, ,constants
please help
Fundamental Existence Theorem for Linear Differential Equations Given an IVP d"y d" y dy +ao(x)ygx) dx ... a1 (x)- + an-1 (x) dx" а, (х) dx"-1 yу-D (хо) — Уп-1 У(хо) %3D Уо, у (хо) — У1, ..., If the coefficients a,(x), ... , ao(x) and the right hand side of the equation g(x) are continuous on an interval I and if a,(x) 0 on I then the IVP has a unique solution for the point xo E...
Find a solution of the IVP dy/dx=xy^3(1+x^2)^-1/2, y(0)=1, and give the interval where the solution is defined.
Please solve both
1 point) A brick of mass 6 kg hangs from the end of a spring. When the brick is at rest, the spring is stretched by 3 cm. The spring is then stretched an additional 4 cm and eleased. Assume there is no air resistance. Note that the acceleration due to gravity-g, is g 980 cm/s Set up a differential equation with initial conditions describing the motion and solve it for the displacement s(t) of the mass...
Theorem 2.1 Consider an IVP of the form y' + g (x)ya h(x), y(%)-yo. Assume that g(x) and h(x) are both continuous on some interval a < x < b and that a < xo < b. Then there exists a unique solution y(x) to the initial value problem that is defined on a <x<b Theorem 2.2 Consider an IVP of the form y' = f (x.y), y(xo) = yo. Assume that ftxy) andfx, y) are both continuous on a...
Example 4 Solve the following IVP and find the interval of validity for the solution. (0) 0
Question 10 Incorrect Mark 0.00 out of 4.00 p Flag question Given the IVP y(0) = 1 Without explicitly solving the ODE, indicate which of the following statements are true. Select one or more: a. The existence and uniqueness theorem guarantees the existence of a unique solution defined in an interval (h, h). b. The existence and uniqueness theorem guarantees the existence of a unique solution defined in an interval (1 - h. 1 + h). X c. The solution...