Find the solution of each of the following initial-value problems.
Find the solution of each of the following initial-value problems. (1)=60x (55%*)+*(== 3)-**
(24 points) Find the solution of each of the following initial value problems: a) xy' + 3y = x V),y(1) = 0 (Bernoulli equation) 18 1 b) y" – 4y - 12y = 3e St, y (0) = , y'(0) - (Hint: use the method of undetermined coefficients) c) (2xy - 9x) dx + (2y + x2 + 1) dy = 0,y (0) = - 3 (Hint: first show this is an exact DE) = -1 7
solve 5c 5. (24 points) Find the solution of each of the following initial value problems: a) xy' + 3y = x V),y (1) = 0 (Bernoulli equation) 18 b) y" – 4y' – 12y = 3e5, y (0) =- (Hint: use the method of undetermined 7 coefficients) c) (2xy - 9x?) dx + (2y + x2 + 1) dy = 0,y (0) = - 3 (Hint: first show this is an exact DE)
(5) Find the solution of the following initial value problems. determine the largest interval in which the solution is va (a) xy + y = ex; y(1) = 1
Problem 1. Find the solution to the following initial value problems. (a) y'" – y" – 4y' + 4y = 0; y(0) = -4, y'(0) = -1, y"(0) = -19. (b) y'' – 4y"' + 7y – by = 0; y(0) = 1, y'(0) = 0, y"(O) = 0.
Differential Equations Question Method of Elimination - Initial Value Problems. Find the solution of the following IVPs. (13) x1 = 4x1 - x2 + 3e2t x1(0) = - x2 = 2x1 + x2 + 2t X2(0) = 42
In problems 7 and 8 find the solution of the given initial value problem in explicit form: 7. sin 2.x dx + cos 3y dy = 0, y /2) = 1/3. 8. y' (1-22)/2 dy = arcsin x dx, y(0) = 1.
3. Use Laplace transforms to solve the following initial value problems. Write the solution (t) for t20 as a simplified piecewise defined function. (a) z', + 2x' + 2x-f(t), x(0-0, z'(0)-i, where f(t)-〈0 otherwise. (b) z', +x-f(t), x(0) 0, z'(0)=1, where t/2 if 0 t< 6, 3 ift26 f(t) 3. Use Laplace transforms to solve the following initial value problems. Write the solution (t) for t20 as a simplified piecewise defined function. (a) z', + 2x' + 2x-f(t), x(0-0, z'(0)-i,...
26 Find the solutions of the following initial-value problems: (a) cos(x + t)| _ + 1 | + 1 0, x(0) π 3 (b) 3(x + 2012ー+ 6(x +21)]/2 + 1 = 0. dt x(-1) 6
do 2 and 3 Example 2.4. Find a solution to the initial value problem tion of variables. = xy'), y(0) = 0 by separa- = 220/2 dx dy =xda yv f yolkdy - freda 1/2 y 2 Vy = 22 + c y colo 200) = 0 + c cao = 25 = 22 - ² - 4 Vy Show that the theorem on eristence and uniqueness of first-order initial value problems (See See ) does not guarantee that this...
1. Show that the following initial value problem has a unique solution and find the solution. -?v+te", ist32, y(1) = 0 (14 pts)