Show the differential equation is not exact and by finding an appropriate integrating factor solve the...

Show the differential equation is not exact and by finding an appropriate integrating factor solve the given initial problem.

(yx+y^2+ y) dx + (x+2y) dy =0

Expert Solution

Colby Messinger answered 2 years ago

Check that the following differential equation is not exact. Find an integrating factor that makes it...

Check that the following differential equation is not exact. Find an integrating factor that makes it exact and solve it. ydx + (3 + 3x-y) dy = 0 __ Solve the initial value problem: (cos xsen x-xy ^ 2) dx + (1-x ^ 2) ydy = 0 if y (0) = 2 __ Solve the initial value problem: y ^ (2) cosx dx + (4 + 5ysenx) dy = 0; y (π / 2) = 1

a) Determine whether the given differential equation is exact. If it is exact, solve it. (If...

a) Determine whether the given differential equation is exact. If it is exact, solve it. (If it is not exact, enter NOT.) (2xy2 − 5) dx + (2x2y + 4) dy = 0 b) Solve the given differential equation by finding, as in Example 4 of Section 2.4, an appropriate integrating factor. (6 − 20y + e−5x) dx − 4 dy = 0

Determine whether the given differential equation is exact. If it is exact, solve it. i) (x...

Determine whether the given differential equation is exact. If it is exact, solve it. i) (x 3 + y 3 )dx + 3xy2 dy = 0, Ans. x 4 + 4y 3x = C ii) (y ln y − e −xy) + (1 y + x ln y) dy dx = 0, Ans. not exact iii) (e −x sin y − 3)dx − (3x 2 − e x sin(2y))dy = 0, Ans. not exact iv) (xy − 1)dx + (x...

Solve each of the following equations by finding an integrating factor: x dy + y dx...

Solve each of the following equations by finding an integrating factor: x dy + y dx + 3x^3y^4 dy = 0

Summarize seperable equations, integrating factor, exact equations, and auxiliary equation in your own words and what...

Summarize seperable equations, integrating factor, exact equations, and auxiliary equation in your own words and what mathematical skills are needed in each technique. Please no handwriting unless I can read it please.

Solve the given differential equation using an appropriate substitution. The DE is a Bernoulli equation, A....

Solve the given differential equation using an appropriate substitution. The DE is a Bernoulli equation, A. dy/dx = y(xy^6 - 1) B. x dy/dx + y = 1/y^2 C. t^2 dy/dt + y^2 = ty

The past few modules introduced various ways to solve a differential equation, separation of variables, integrating...

The past few modules introduced various ways to solve a differential equation, separation of variables, integrating factor, and exact equations. As you can see, you need skills from previous coursework, in particular algebraic manipulation and both differentiation and integration, to solve these equations. How do these skills translate to differential equations? In a general sense, explain how algebra, differentiation, and integration skills are necessary to classify and solve first-order ODEs. Include an example in your explanation.

Question 3: Exact Differential Equation i. Test to see if the following equation is exact, if...

Question 3: Exact Differential Equation i. Test to see if the following equation is exact, if exact solve for the general solution (??/??) +(2? ????+?^3?^?)/(?^2cos?+3?^2?^?)=0 ii. Solve (?+????)??+(?????−2?)??=0 iii. Solve (?^2+?)??+(?^?−?)??=0 iv. (2?−3?)??+(2?−3?)??=0 I am sorry I could not send a photo. Whenever I try from the app it posts another question on the same page. I tried doing them individually and the only thing that happened was that the same question got posted 4 times. I would appreciate your...

1. Set-up the appropriate differential equation(s) and solve to derive the general equation of motion for...

1. Set-up the appropriate differential equation(s) and solve to derive the general equation of motion for a human sized “dummy” moving vertically (up/down) under the following assumptions: (a)The initial elevation is h0 ft. (b)The initial velocity is V0 ft./sec. (c)All motion vertical (ignore any sideways motion). (d)The force due to wind is proportional to velocity and in the opposite direction of velocity. (e)The “terminal velocity” is 120mph (e.g. lim t→∞ (V)= 120 mph). (f)Force = Mass * Acceleration. (g)Acceleration due to...

Solve the given differential equation by using an appropriate substitution. The DE is homogeneous. dy dx...

Solve the given differential equation by using an appropriate substitution. The DE is homogeneous. dy dx = y − x y + x

Question