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April 13, 2020 MATH2107- MIDTERM EXAM.I/1 Q.1(40 pts) Find the solutions of the following differential equa-...
(24 points) Find the solution of each of the following initial value problems: a) xy' +...
(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:...
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)
2. Show that the differential equation below is exact and find the general solution. (2xy +...
2. Show that the differential equation below is exact and find the general solution. (2xy + 2 y) dx + (2x+y+2x)dy-0
Use the method of characteristics to find solutions to the following first-order partial differential equa- tions...
Use the method of characteristics to find solutions to the following first-order partial differential equa- tions (PDEs): V_zī ar +Ou-0, (a) [10 points] u(0,y)-y. (b) [10 pointsj (0,y) - sin y
3.2 Problems Find general solutions in powers of x of the diferential equa- tions in Problems 1 t...
5 please
and 17 only
3.2 Problems Find general solutions in powers of x of the diferential equa- tions in Problems 1 through 15. State the recurrence relation and the guaranteed radius of convergence in each case. 1, (x2-1 )y', + 4xy' + 2y = 0 2. (x2 + 2)y', + 4xy' + 2y = 0 3. y+xy y 0 4. (x2 + 1)y', + 6xy' + 4y = 0 5. (x2 3)y' +2xy 0 Use power series to solve...
solve differential equation If - Dord, find y @ (5,12) dy + 2xy = 6xe*** (11...
solve differential equation
If - Dord, find y @ (5,12) dy + 2xy = 6xe*** (11 pts) dx 4. dx + x* ydy = 0
(1 point) Use the "mixed partials" check to see if the following differential equation is exact....
(1 point) Use the "mixed partials" check to see if the following differential equation is exact. If it is exact find a function F(x, y) whose differential, d F(x, y) is the left hand side of the differential equation. That is, level curves F(x, y) = C are solutions to the differential equation (-3e* sin(y) + 4y)dx + (4x – 3e* cos(y))dy = 0 First, if this equation has the form M(x, y)dx + N(x, y)dy = 0: My(x, y)...
14. Find the integrating factor p so that the non-exact differential equation becomes exact (2 Points)...
14. Find the integrating factor p so that the non-exact differential equation becomes exact (2 Points) (2x + tan y) dx + (x - x2 tan y) dy = 0 O u = csc y O u = - tan y O u = cos y O u = sec y This question is required.
(1 point) Use the "mixed partials" check to see if the following differential equation is exact....
(1 point) Use the "mixed partials" check to see if the following differential equation is exact. If it is exact find a function F(x, y) whose differential, dF(, y) gives the differential equation. That is, level curves F(x,y) = C are solutions to the differential equation: dy 4x3 - y dx + 4y2 First rewrite as M(x,y) dic + N(x, y) dy = 0 where M(x,y) = and N(x,y) = If the equation is not exact, enter not exact, otherwise...
(1 point) Use the "mixed partials" check to see if the following differential equation is exact....
(1 point) Use the "mixed partials" check to see if the following differential equation is exact. If it is exact find a function F(x,y) whose differential, dF(x, y) is the left hand side of the differential equation. That is, level curves F(x, y) - C are solutions to the differential equation (-le sin(y)-3y)ax + (-3x + 1e' cos(y))dy-0 First: M,(x,y) = and N,( If the equation is not exact, enter not exact, otherwise enter in F(x, y) here
(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)
2. Show that the differential equation below is exact and find the general solution. (2xy + 2 y) dx + (2x+y+2x)dy-0
Use the method of characteristics to find solutions to the following first-order partial differential equa- tions (PDEs): V_zī ar +Ou-0, (a) [10 points] u(0,y)-y. (b) [10 pointsj (0,y) - sin y
5 please
and 17 only
3.2 Problems Find general solutions in powers of x of the diferential equa- tions in Problems 1 through 15. State the recurrence relation and the guaranteed radius of convergence in each case. 1, (x2-1 )y', + 4xy' + 2y = 0 2. (x2 + 2)y', + 4xy' + 2y = 0 3. y+xy y 0 4. (x2 + 1)y', + 6xy' + 4y = 0 5. (x2 3)y' +2xy 0 Use power series to solve...
solve differential equation
If - Dord, find y @ (5,12) dy + 2xy = 6xe*** (11 pts) dx 4. dx + x* ydy = 0
(1 point) Use the "mixed partials" check to see if the following differential equation is exact. If it is exact find a function F(x, y) whose differential, d F(x, y) is the left hand side of the differential equation. That is, level curves F(x, y) = C are solutions to the differential equation (-3e* sin(y) + 4y)dx + (4x – 3e* cos(y))dy = 0 First, if this equation has the form M(x, y)dx + N(x, y)dy = 0: My(x, y)...
14. Find the integrating factor p so that the non-exact differential equation becomes exact (2 Points) (2x + tan y) dx + (x - x2 tan y) dy = 0 O u = csc y O u = - tan y O u = cos y O u = sec y This question is required.
(1 point) Use the "mixed partials" check to see if the following differential equation is exact. If it is exact find a function F(x, y) whose differential, dF(, y) gives the differential equation. That is, level curves F(x,y) = C are solutions to the differential equation: dy 4x3 - y dx + 4y2 First rewrite as M(x,y) dic + N(x, y) dy = 0 where M(x,y) = and N(x,y) = If the equation is not exact, enter not exact, otherwise...
(1 point) Use the "mixed partials" check to see if the following differential equation is exact. If it is exact find a function F(x,y) whose differential, dF(x, y) is the left hand side of the differential equation. That is, level curves F(x, y) - C are solutions to the differential equation (-le sin(y)-3y)ax + (-3x + 1e' cos(y))dy-0 First: M,(x,y) = and N,( If the equation is not exact, enter not exact, otherwise enter in F(x, y) here
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