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previous $7.1 - Level 1 2. Suppose we have a function with the graph...
We have found the complementary function for the given nonhomogeneous differential equation. Now we must find...
We have found the complementary function for the given nonhomogeneous differential equation. Now we must find the particular solution, which will be based on the form of the function of x that makes the equation nonhomogeneous, g(x) = 200x2 – 78xe. The idea is that when the partial solution y, (and its derivatives) is substituted into the equation, it must be equal exactly to g(x). Therefore, we can assume the solution contains a quadratic expression and an exponential term. Assume...
1. Consider the function. (a) Draw the level curves of this function for levels c = 0, 1, 2. Please clearly label each level curve with the appropriate value of c. (b) Use the previous answer to sketc...
1. Consider the function. (a) Draw the level curves of this function for levels c = 0, 1, 2. Please clearly label each level curve with the appropriate value of c. (b) Use the previous answer to sketch the graph (c) Find all first and second order derivatives of this function. (Please label all your derivatives clearly.) (d) Find the equation of the tangent plane to 2.. Let (a) Show that does not exist. (b) Show that does exist and...
Solve question 2. Question 1 posted below for reference 2. a. If f(t) in the previous...
Solve question 2. Question 1 posted below for reference
2. a. If f(t) in the previous question was replaced by an impulse function at t2. Can you re-write the differential equation in the last problem? b. Determine the response to the force impulse at t=2 s. 1. a Can you write the function given in figure 1 as a Fourier series? Why? Af(t) 1 2 3 4 5 6 7 Figure 1 b. If your answer to the previous question...
Question 2 Consider the differential equation We saw in class that one solution is the Bessel function (a) Suppose we h...
Question 2 Consider the differential equation We saw in class that one solution is the Bessel function (a) Suppose we have a solution to this ODE in the form y-Σχ0CnXntr where cn 0. By considering the first term of this series show that r must satisfy r2-4-0 (and hence that r = 2 or r =-2) (b) Show that any solution of the form y-ca:0G,2n-2 must satisfy C0 (c) From the theory about singular solutions we know that a linearly...
Suppose a function E:R → R is defined as the solution of the ODE E'(x) = -TE(), E(0) = 1. We will assume that this equa...
Suppose a function E:R → R is defined as the solution of the ODE E'(x) = -TE(), E(0) = 1. We will assume that this equation has a solution, and that Ex) #0 for all x E R. For this problem, you are to answer all the equations without solving the differential equationforget that you might be able to do this! (a) Prove that E(x) > 0 for all x (recall: we assume E(x) + 0). (b) Use the mean...
Below is the graph of the function y(x) which is a solution to the differential equation...
Below is the graph of the function y(x) which is a solution to
the differential equation dy dx = f(x, y).
please help me, thanks so much
Below is the graph of the function y(I) which is a solution to the differential equation due = f(,y). The 2-values of the labeled points below are -3, -2, and 1.7 respectively. Suppose that for geometric reasons we also know the y-values of points A and B. I wish to use Euler's method...
[Question 1] Find and graph the domain of the function f(,y)-In-) Question 2] Graph a contour map...
[Question 1] Find and graph the domain of the function f(,y)-In-) Question 2] Graph a contour map of the function f(z, y)2s y 1 that contains four level curves. Make sure to find an equation for each level curve and label each one on the graph. IQuestion 3] The equation of the tangeat plane to the function z the equation: Using the form of the equatioa above, fiud the tangent plane to f(a,y)yat the point (2. ). Question 4] Find...
Problem List Next Problem Previous Problem (1 point) In this problem we consider an equation in...
Problem List Next Problem Previous Problem (1 point) In this problem we consider an equation in differential form M dx + N dy = 0 (5х + 7у)dx - (7x + 3у)dy %3D0 Find М, If the problem 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, give implicit general solutions to the differential equation. If the equation is not exact,...
Sketch the graph of the following function. Describe how the graph can be obtained from the...
Sketch the graph of the following function. Describe how the graph can be obtained from the graph of the basic exponential function e Ay 8- 6- 4- 2- f(x)= 2 (3-ex) Use the graphing tool to graph the equation. 6 -4 10 Click to enlarge graph Describe how the graph can be obtained from the graph of the exponential function eX. Choose the correct answer below. O A. Reflect the graph of y s thex-axis, shift it up and shrink...
3. We consider differential equations of the form (a) Suppose we have found (by some means)...
3. We consider differential equations of the form (a) Suppose we have found (by some means) a solution yi(t) of equation (1). Verify that y(t)-yi(t)+w(t) is also a solution of (1) where w is any function which satisfies Notice this shows that the general solution of (1) can be found if we know at least one particular solution of (1) and the general solution of (2). Moreover, the general solution of (2) can be found by using the method of...
We have found the complementary function for the given nonhomogeneous differential equation. Now we must find the particular solution, which will be based on the form of the function of x that makes the equation nonhomogeneous, g(x) = 200x2 – 78xe. The idea is that when the partial solution y, (and its derivatives) is substituted into the equation, it must be equal exactly to g(x). Therefore, we can assume the solution contains a quadratic expression and an exponential term. Assume...
Solve question 2. Question 1 posted below for reference
2. a. If f(t) in the previous question was replaced by an impulse function at t2. Can you re-write the differential equation in the last problem? b. Determine the response to the force impulse at t=2 s. 1. a Can you write the function given in figure 1 as a Fourier series? Why? Af(t) 1 2 3 4 5 6 7 Figure 1 b. If your answer to the previous question...
Question 2 Consider the differential equation We saw in class that one solution is the Bessel function (a) Suppose we have a solution to this ODE in the form y-Σχ0CnXntr where cn 0. By considering the first term of this series show that r must satisfy r2-4-0 (and hence that r = 2 or r =-2) (b) Show that any solution of the form y-ca:0G,2n-2 must satisfy C0 (c) From the theory about singular solutions we know that a linearly...
Suppose a function E:R → R is defined as the solution of the ODE E'(x) = -TE(), E(0) = 1. We will assume that this equation has a solution, and that Ex) #0 for all x E R. For this problem, you are to answer all the equations without solving the differential equationforget that you might be able to do this! (a) Prove that E(x) > 0 for all x (recall: we assume E(x) + 0). (b) Use the mean...
Below is the graph of the function y(x) which is a solution to
the differential equation dy dx = f(x, y).
please help me, thanks so much
Below is the graph of the function y(I) which is a solution to the differential equation due = f(,y). The 2-values of the labeled points below are -3, -2, and 1.7 respectively. Suppose that for geometric reasons we also know the y-values of points A and B. I wish to use Euler's method...
[Question 1] Find and graph the domain of the function f(,y)-In-) Question 2] Graph a contour map of the function f(z, y)2s y 1 that contains four level curves. Make sure to find an equation for each level curve and label each one on the graph. IQuestion 3] The equation of the tangeat plane to the function z the equation: Using the form of the equatioa above, fiud the tangent plane to f(a,y)yat the point (2. ). Question 4] Find...
Problem List Next Problem Previous Problem (1 point) In this problem we consider an equation in differential form M dx + N dy = 0 (5х + 7у)dx - (7x + 3у)dy %3D0 Find М, If the problem 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, give implicit general solutions to the differential equation. If the equation is not exact,...
Sketch the graph of the following function. Describe how the graph can be obtained from the graph of the basic exponential function e Ay 8- 6- 4- 2- f(x)= 2 (3-ex) Use the graphing tool to graph the equation. 6 -4 10 Click to enlarge graph Describe how the graph can be obtained from the graph of the exponential function eX. Choose the correct answer below. O A. Reflect the graph of y s thex-axis, shift it up and shrink...
3. We consider differential equations of the form (a) Suppose we have found (by some means) a solution yi(t) of equation (1). Verify that y(t)-yi(t)+w(t) is also a solution of (1) where w is any function which satisfies Notice this shows that the general solution of (1) can be found if we know at least one particular solution of (1) and the general solution of (2). Moreover, the general solution of (2) can be found by using the method of...
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