Consider the second order equation r" + 2.3-r2-2x = 0. (a) Put y-', and transform the second order equation into an equivalent system of first order equations for (x(t), y(t system Find al critical (equilibrium) points for the (b) For each critical point of the systern from part (a), use linearization to determine the local behaviour (if possible) and stability (if possible) of the critical point. Ski (lı ile 1",lobal phase portrait of the stem frolll pari a Dei ermine...
2. Transform the following differential equation into an equivalent system of first-order differential equations 2-(3) – 3r(2) – 4.x' + 2x² = 2 cos 4t
2. Transform the following differential equation into an equivalent system of first-order differential equations 2-(3) – 3r(2) – 4.x' + 2x² = 2 cos 4t
transform the given differential equation or system into an equivalent system of first order differential equation x"+3x²+48-2y=0 y"+24'-3x+y = cost
Transform the given system into a single equation of second-order x'= -821 + 7:02 2 = -721 - 822- Then find 21 and 22 that also satisfy the initial conditions Then find 2, and are that alene 21 (0)=9 22 (0) = 2. Enter the exact answers. Enclose arguments of functions in parentheses. For example, sin (23).
7. Use the Laplace transform to solve the system dx dt -x + y dy = 2x dt x(0) = 0, y(0) = 1
(1 point) Consider the differential equation 2x(x )y"3 - 1)y -y0 which has a regular singular point atx 0. The indicial equation for x 0 is 2+ 0 r+ with roots (in increasing order) r and r2 Find the indicated terms of the following series solutions of the differential equation: x4. (a) y =x (9+ x+ (b) y x(7+ The closed form of solution (a) is y (1 point) Consider the differential equation 2x(x )y"3 - 1)y -y0 which has...
16. Solve the IVP with a Laplace transform method x" + 2x' + 2x = e-t, x(0) = 1, x'(0) = 1
Each of the following equation represents an unforced damped oscillator. Write the Laplace transform of the characteristic equation. And define if the system is over-damped, under-damped or critically damped. 1) 23 + 4 + 2x = 0 2) 3 +43 +3.2 = 0 3) 43 + 7 + 5x = 0 BIU A - A - IX E 33 x X, DE EV G* T 1 12pt Paragraph
1.4. Solve the differential equation tx"– 2x' =0, x(1) = 7, x'(1)=6.