Solve by Green function: y'' + y = tsin t
Solve the exact differential equation (4 x y tsin x) dx + (x" - Y) dy = 0
(1 point) A. Solve the following initial value problem: dy dt cos (t)-1 with y(6) tan(6). (Find y as a function of t.) (1 point) A. Solve the following initial value problem: dy dt cos (t)-1 with y(6) tan(6). (Find y as a function of t.)
y(t)=? Solve the following differential equation by Laplace transforms. The function is subject to the given conditions. y'' +81y = 0, y(0) = 0, y'(0) = 1 Click the icon to view the table of Laplace transforms. y = (Type an expression using t as the variable. Type an exact answer.)
Solve the nonhomogeneous IBVP Using the Fourier transformation and Green function
Determine the form of a particular solution for the differential equation. Do not solve. y" - 18y' + 82y = et + tsin 2t - cos 2t The form of a particular solution is yp(t)= (Do not use d D. e. Ei or las arbitrary constants since these letters already have defined meanings.)
Solve the IVP y' + y = f(t), y(0) = 0, where f is the 27-periodic function given by f(t) -1, 0<t<T, <t<21, f(t) = f(t + 27).
The Green function G(x, a') for a particle in an attractive one dimensional potential V(x) _λδ(x) satisfies the following equation (a) Solve for the Green function G(x,'). (b) Show that G diverges (a simple pole) at a particular energy Eo and find its value. The Green function G(x, a') for a particle in an attractive one dimensional potential V(x) _λδ(x) satisfies the following equation (a) Solve for the Green function G(x,'). (b) Show that G diverges (a simple pole) at...
3. Solve y" + 2ay' +y -sin(t) with initial condition y(0) -y'(0)0 for all values of a 2 0. Plot the amplitude of oscillations as a function of w for α-1/2 W1 3. Solve y" + 2ay' +y -sin(t) with initial condition y(0) -y'(0)0 for all values of a 2 0. Plot the amplitude of oscillations as a function of w for α-1/2 W1
Green's function 2 The Green function (10 P) The Fourier transform plays a tantamount role in the theory of inhomogeneous, linear differential equations. If as was shown in the lecture - G is a so called fundamental solution of the differential equation CG(z,z') = δ(z-z') one may calculate a particular solution for an inhomogeneity g by convolution G is called Green function. Since the Fourier transform maps derivatives to multiplications, it simplifies the calcu- lation of the Green function to...
Solve \(y(t)\) given$$ y^{\prime}(t)+\int_{0}^{t} e^{2 \tau} y(t-\tau) d \tau=1, \quad y(0)=0 $$