Given DE is of the form
M(x,y)dx+N(x,y)dy=0
Now use condition of exactness
which doesn't hold hence given DE is not exact.
1) Consider the following equation. 6xy dx (4y 9x2)dy-0 a) Show the equation is not exact....
SORU 15 the differential equation is exact. (9x2 +3y?)dx+(6xy+9y?)dy=0 Dogru O Yarilis SORU 16
Consider the equation 2xy (y dx + x dy) = (y dx - xdy) sin - Is the equation exact? If not, find an integrating factor, and solve the equation that is exact with the integrating factor
[8] 2. Consider the differential equation dx + (1 - sin(v)) dy = 0 Determine if the equation is exact. If so, solve. If not determine an approximation integrating acco the equation exact. Verify that the new equation is exact, and solve the differential equation using the integrating factor you have found. (Hint: the integrating factor should be a function of y only.)
Find an integrating factor of the form x"y" and solve the equation. (2x y-9y)dx + (4y -9x)dy 0 by multiplying by the integrating factor. An implicit solution in the form F(x,y) C is C, where C is an arbitrary constant, and (Type an expression using x and y as the variables.) Find an integrating factor of the form x"y" and solve the equation. (2x y-9y)dx + (4y -9x)dy 0 by multiplying by the integrating factor. An implicit solution in the...
a) Consider the first-order differential equation (y + cos.r) dx + dy = 0. By multiplying integrating factor y(x) = ei" to both sides, show that the differential equation is exact. Hence, solve the differential equation. (6 marks) b) Solve the differential equation (4.r + 5)2 + ytan z = dc COSC (7 marks)
Consider the following differential equation. (x2 − 4) dy dx + 4y = (x + 2)2 Consider the following differential equation. dy (x2 - 4) dx + 4y = (x + 2)2 Find the coefficient function P(x) when the given differential equation is written in the standard form dy dx + P(x)y = f(x). 4 P(x) = (x2 – 4) Find the integrating factor for the differential equation. SP(x) dx 1 Find the general solution of the given differential equation....
Solve the following exact differential equation with initial value. (5x + 4y)dx + (4x - 8y3)dy = 0, y(0) = 2
Exercise 2 (4 marks) Consider the equation, (2y 6x)dr + (3r - 4xy 1)dy 0 1. Is it exact? 2. Use a special integrating factor to solve the equation. Exercise 2 (4 marks) Consider the equation, (2y 6x)dr + (3r - 4xy 1)dy 0 1. Is it exact? 2. Use a special integrating factor to solve the equation.
In this problem we consider an equation in differential form M dx + N dy = 0. The equation (2е' — (16х° уе* + 4e * sin(x))) dx + (2eY — 16х*y'е*)dy 3D 0 in differential form M dx + N dy = 0 is not exact. Indeed, we have For this exercise we can find an integrating factor which is a function of x alone since м.- N. N can be considered as a function of x alone. Namely...
Consider the differential equation: cos(x)dx + (9+ 6y) sin(x)dy = 0 Which of the following can be an integrating factor to make the equation exact? Select all that apply. =csc(x) Ou = 9y+3y2 OH= - cot(a) Ou = €9+67