Yep you are right, we are helping each other out... actually we have the problems in a multiple choice format, but we cant get the answers, if u may help us... here is the list of problems with the choices,...
tnx
Question2
In (dy/dx) + yP(x) = y^n Q(x), if n = 1 the equation would be reduced to a
A Bernoulli Equation
B Exact equation
C Variable Separable
question 3
Question3 Transform 2xdy - y(x+1)dx + 6y^3dx = 0 into a Bernoulli Equation.
A (dy/dx) - y(1+ 1/x) = 3y^3(1/x)
B y ' - [y(x + 1)/2x] = 3y^3/x
C (dy/dx) - (x + 1)/xy^2 = (3/2x)
question 4
Question4 The slope of the normal line to y^2 = x/2 at P(1/8,1/4) is ____.
A 1/16
B -1/8
C -1/4
question 5
Question5 The orthogonal trajectory of y^2 - x^2 = C is___.
A ln y/x = C
B xy = c
C lny = lnx + C
question 6
Question6 The given functions cos x, sin x, and
cos (x-pi/6) are said to be _____.
A linearly dependent
B linearly independent
C a relation
question 7
Question7 If the Wronskian of the given functions is not equal to 0, then the functions are said to be____.
A linearly dependent
B linearly independent
C inconsistent
question 8
Question8 The functional determinant of x, e^x, and e^-x is equal to___.
A 0
B 2
C 2x
question 9
Question9 The equation of the tangent line of the one-family of curve x^2 + y^2 = 25 at
P(4, 3) is _______.
A 4x -3y + 25 = 0
B 4x + 3y - 25 = 0
C 3x + 4y -24 = 0
Question10 The complete solution of 2x^3 dy = y (y^2 + 3x^2) is _____.
A y^2 = (c - x) x^3
B y^2 (c - x ) = x^3
C x^2 (c -x) = y^3
-------------------------------
help...
Many of the questions listed have already been posted separately. This is good, because this will give you the best chances of getting answers in the shortest time, most of the time by different teachers.
However, if the questions come from the same person, it would be advantageous to post using the same name, because teachers will have the latitude of referring to previously solved problems, and the student will benefit from the continuity.
Many of the questions have been answered. So it is a matter of time that the remaining questions will be responded.
It is also important to note that what we offer here is help, not answers. The students have to put in their shares to benefit from the learning process. In general, that means that students have to post their work and identify where help is needed.
Question2
In (dy/dx) + yP(x) = y^n Q(x), if n = 1 the equation would be reduced to a
A Bernoulli Equation
B Exact equation
C Variable Separable
When n=1, the equation reduces to:
y' + yP(x) = yQ(x)
y' = y(P(x)+Q(x))
y'/y = P(x) + Q(x)
Does that look familiar to you?
The answers to Q7 and Q8 can be found in the following article, which should resemble your class notes.
http://en.wikipedia.org/wiki/Wronskian
Sure, I can help you with these multiple-choice questions. Here's how you can approach each question to find the correct answer:
Question 2:
The given equation is (dy/dx) + yP(x) = y^n Q(x), and we are told that n = 1. To determine the type of equation it becomes, substitute n = 1 in the equation. If n = 1, the equation will be reduced to yQ(x) = (dy/dx) + yP(x). Comparing this with the standard form of a Bernoulli Equation, which is dy/dx + P(x)y = Q(x)y^n, we can see that the equation becomes a Bernoulli Equation. So the correct answer is A) Bernoulli Equation.
Question 3:
The given equation is 2xdy - y(x+1)dx + 6y^3dx = 0, and we need to transform it into a Bernoulli Equation. To do this, divide the entire equation by dx and rearrange terms. After rearranging, the equation becomes (2x/y)dy - (x + 1)dx + 6y^3dx = 0. This equation is in the form dy/dx - P(x)y = Q(x)y^n, which is the standard form of a Bernoulli Equation. So the correct answer is A) (dy/dx) - y(1+ 1/x) = 3y^3(1/x).
Question 4:
The equation of the given curve is y^2 = x/2, and we need to find the slope of the normal line at point P(1/8, 1/4). To find the slope of the normal line, we take the derivative of the equation y^2 = x/2 with respect to x, and then substitute the x-coordinate of the point P. After finding the derivative and substituting the values, we get the slope as -1/8. So the correct answer is B) -1/8.
Question 5:
The given equation is y^2 - x^2 = C, and we need to find the orthogonal trajectory. To find the orthogonal trajectory, we interchange x and y and change the sign of one of them. After making these changes, the equation becomes x^2 - y^2 = C. This equation represents a hyperbola, and its orthogonal trajectory is a set of straight lines given by y = mx, where m is the slope of the line. So the correct answer is B) xy = c.
Question 6:
The given functions are cos(x), sin(x), and cos(x-pi/6). To determine if they are linearly dependent or independent, we can create a linear combination of them and see if it equals zero. By considering the trigonometric identity cos(x-pi/6) = cos(x)cos(pi/6) + sin(x)sin(pi/6), we can see that cos(x-pi/6) can be written as a linear combination of cos(x) and sin(x). Therefore, the given functions are linearly dependent. So the correct answer is A) linearly dependent.
Question 7:
For the given functions, if the Wronskian is not equal to zero, then the functions are said to be linearly independent. The Wronskian is a determinant formed from the functions and their derivatives. So the correct answer is B) linearly independent.
Question 8:
To find the functional determinant of x, e^x, and e^-x, we form a matrix with these functions as the columns and take its determinant. The resulting determinant is -2. Therefore, the correct answer is not listed in the options provided.
Question 9:
The equation of the tangent line to a curve at a given point can be found by taking the derivative of the equation of the curve and substituting the coordinates of the given point. For the one-family of curves x^2 + y^2 = 25, the derivative with respect to x is 2x + 2y(dy/dx) = 0. After substituting the given point P(4, 3) into the derivative, we get the tangent line equation as 4x - 3y + 25 = 0. So the correct answer is A) 4x - 3y + 25 = 0.
Question 10:
The given differential equation is 2x^3 dy = y (y^2 + 3x^2). To solve this equation, we can separate variables and integrate both sides. After integrating and simplifying, we get y^2 = (c - x) x^3. So the correct answer is A) y^2 = (c - x) x^3.
Hope this helps you find the correct answers to each question. Let me know if you have any further questions!