Solve the initial value problem for r as a vector function of t. dr Differential equation:...
Solve the initial value problem for r as a vector function of t. dr Differential equation: = -32k . = 21 + 2] Initial conditions: r(0) = 60k and r(t) = (i+1+OK
Solve the following initial value problem for r as a function of t. Differential equation: Initial conditions: dar -= 3e ti -2e - tj + 9e 3tk dt? r(0) = 71 + 2 + 4k dr = - +5j dt 0
(1 point) Find the solution r(t) of the differential equation with the given initial condition: r' (t) = (sin 2t, sin 5t, 3t) , r(0) = (5,8,6) r(t) =(
Solve the vector valued differential equation below, dr dt2 -(i+j+ k) subject to following initial conditions: 7(0) = 10i + 10j + 10k dr and = 0 delt=0
8. The position vector r of a point P is a function of the time t and r satisfies the vector differential equation d2r dr 2k (k2 n2)r g, dr2 where k and n are constants and g is a constant vector. Solve dr a and dt this differential equation given that r v when t = 0, a and v being constant vectors Show that P moves in a plane and write down the vector equation of this plane...
fx px 3. Solve the following initial value problem (13.2.20): Differential Equation: = (sin t) î - (cost)ġ + (4 sint cost)k Initial Conditions: (0) = î - R op (0) = î
2. Solve the initial value problem for the given differential equation. 2. Solve the initial value problem for the given differential equation.
Evaluate the line integral ∫ F *dr where C is given by the vector function r(t). F(x, y, z) = (x + y2) i + xz j + (y + z) k, r(t) = t2i + t3j − 2t k, 0 ≤ t ≤ 2
(a) Solve the initial value problem 2" +2r' + r = 8(t - 2), z(0)=1, 2'0) = 2 (b) Consider the initial value problem -2 -5 z(0) = 3 Find ö(t), writing your answer as a single vector. k 2 k 0 1] (c) Consider the matrix 0 -2 k 3 i. Compute the determinant. ii. For what value(s) of k does A exist? iii. For what value(s) of k does the linear system A7 = 7 have nontrivial solutions?...
8. Solve the following differential equation given the initial condition y(0) = -5: dy 2.c dr 1+22 9. Solve the following differential equation using the method of separation of variables: dy = x²y. dic