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3. Let y" +2y' - 3y = f(x). Find the solution in the cases (a) f(x)=0;...
Consider the vector field F(x, y, z) = 8x^2 + 3y, −5x^2y − 4y^2, 6x^2 + 7y − 8 which is defined on all of double-struck R3, and let F be the rectangular solid region F = {(x, y, z) | 0 ≤ x ≤ a, 0 ≤ y...
Consider the vector field F(x, y, z) = 8x^2 + 3y, −5x^2y − 4y^2, 6x^2 + 7y − 8 which is defined on all of double-struck R3, and let F be the rectangular solid region F = {(x, y, z) | 0 ≤ x ≤ a, 0 ≤ y ≤ b, −1 ≤ z ≤ 1} where a > 0 and b > 0 are constants. Determine the values of a and b that will make the flux of F...
1.Find the general solution to the following ODE's a). y'' +y= sec^2t b). x^2y'' +3xy'+3y=0
1.Find the general solution to the following ODE's a). y'' +y= sec^2t b). x^2y'' +3xy'+3y=0
Let f(x,y) = cx( 1-y), 0 < x < 2y < 1, zero elsewhere. a) Find...
Let f(x,y) = cx( 1-y), 0 < x < 2y < 1, zero elsewhere. a) Find c. b) Are X and Y independent? Why or why not? c) Find PX +Y05)
3. Divergence Find the divergence of: a) Ē(x, y, z)=(-2y x 0] b) F(x,y,z)= (y2 –...
3. Divergence Find the divergence of: a) Ē(x, y, z)=(-2y x 0] b) F(x,y,z)= (y2 – 2x 5x’y x+37] c) v =[3y–2yx xy? -62?x]
3. (20 p.) Let 2x-2y + 6z = 18 , 3y =-6x + 15 and -9z...
3. (20 p.) Let 2x-2y + 6z = 18 , 3y =-6x + 15 and -9z + x +2y-7-0. Solve this linear equation system for variable y by using Cramer rule.
Find the solution of the given IVP y" + 3y' + 2y = Uz(t); y(0) =...
Find the solution of the given IVP y" + 3y' + 2y = Uz(t); y(0) = 0, y'(0) = 1 + e-(t+2) e-2(t+2) + e 2 a. y=et-e-t + uz(t) [+ b. y=et +e-+ + uz(t) [ – e-(6-2) + že=2(t-2)] c. y = e-t-e-2t + uz(t) (2) - e-(4-2) + že=2(t-2)] + d. None of these
7. Given the initial-value problem y" + 3y' + 2y = 4x2, y(0) = 3, y'0)...
7. Given the initial-value problem y" + 3y' + 2y = 4x2, y(0) = 3, y'0) = 1, a. Find its homogeneous solution using the Constant Coefficient approach (10pts) b. Find is particular solution using the Annihilator method. (10pts) c. Find the general solution that satisfies the initial conditions. (5pts)
Find the solution of the given IVP y" + 3y' + 2y = uz(t); y(0) =...
Find the solution of the given IVP y" + 3y' + 2y = uz(t); y(0) = 0, y'(0) = 1 a. y = et-e-t + uz(t) [] + e-(6+2) +22(6+2) b. y = ef +e-t+uz(t)ſ - e-(6-2) + şe-26-2)] + uz(t) - e-(1-2) 3e=2(-2)] e + C. y = e-t-e-27 d. None of these
3. Find m for which the following lines do not form a triangle. x+2y 5D, 2x-3y-4 .2, mx+y 0 [Sol] Since line 3 pass...
3. Find m for which the following lines do not form a triangle. x+2y 5D, 2x-3y-4 .2, mx+y 0 [Sol] Since line 3 passes through the origin, lines D, 2 and 3will not form a triangle in the following three cases: wor When D and 3 are (i) parallel. doa When 2 and 3 are (ii) parallel. When D, and 3 all intersect at one point. (ii Therefore, from ( i ), (ii) and (iii), m 4. Find a for...
2. x+4y= 14 2x - y=1 x=2, y=3 3. 5x + 3y = 1 3x +...
2. x+4y= 14 2x - y=1 x=2, y=3 3. 5x + 3y = 1 3x + 4y = -6 x=2, y=-3 | 4, 2y- 6x =7 3x - y=9 No solution/Parallel lines
Let f(x,y) = cx( 1-y), 0 < x < 2y < 1, zero elsewhere. a) Find c. b) Are X and Y independent? Why or why not? c) Find PX +Y05)
3. Divergence Find the divergence of: a) Ē(x, y, z)=(-2y x 0] b) F(x,y,z)= (y2 – 2x 5x’y x+37] c) v =[3y–2yx xy? -62?x]
3. (20 p.) Let 2x-2y + 6z = 18 , 3y =-6x + 15 and -9z + x +2y-7-0. Solve this linear equation system for variable y by using Cramer rule.
Find the solution of the given IVP y" + 3y' + 2y = Uz(t); y(0) = 0, y'(0) = 1 + e-(t+2) e-2(t+2) + e 2 a. y=et-e-t + uz(t) [+ b. y=et +e-+ + uz(t) [ – e-(6-2) + že=2(t-2)] c. y = e-t-e-2t + uz(t) (2) - e-(4-2) + že=2(t-2)] + d. None of these
7. Given the initial-value problem y" + 3y' + 2y = 4x2, y(0) = 3, y'0) = 1, a. Find its homogeneous solution using the Constant Coefficient approach (10pts) b. Find is particular solution using the Annihilator method. (10pts) c. Find the general solution that satisfies the initial conditions. (5pts)
Find the solution of the given IVP y" + 3y' + 2y = uz(t); y(0) = 0, y'(0) = 1 a. y = et-e-t + uz(t) [] + e-(6+2) +22(6+2) b. y = ef +e-t+uz(t)ſ - e-(6-2) + şe-26-2)] + uz(t) - e-(1-2) 3e=2(-2)] e + C. y = e-t-e-27 d. None of these
3. Find m for which the following lines do not form a triangle. x+2y 5D, 2x-3y-4 .2, mx+y 0 [Sol] Since line 3 passes through the origin, lines D, 2 and 3will not form a triangle in the following three cases: wor When D and 3 are (i) parallel. doa When 2 and 3 are (ii) parallel. When D, and 3 all intersect at one point. (ii Therefore, from ( i ), (ii) and (iii), m 4. Find a for...
2. x+4y= 14 2x - y=1 x=2, y=3 3. 5x + 3y = 1 3x + 4y = -6 x=2, y=-3 | 4, 2y- 6x =7 3x - y=9 No solution/Parallel lines
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