Given the differential equation (2r cosx – 1)r'=r?sin x, obtain the value of U = M dx A U=-r-sin x +f (r) B U =r?cos x+f (r) (C) U=r?sin x+f (r) D U = -r?cos x + f(r)

Q: Let y' (x) = V1– y²(x) be a differential equation. What is a solution? Select one: a. sin(x) b. e" O…

A: Let the given differential equation is:

Q: State the order of the given ordinary differential equation. (sin(0))y"' - (cos(0))y' = 5 Determine…

A: Recall:  1 Order of a differential equation. The order of the highest        order derivative in…

Q: Find the particular solutions of the given differential equation dy dz 2 cos a sin a given y = 1…

A: 1. Sin(2A)=2sin(A)cos(A). 2. Sin²A+Cos²A=1.

Q: 3. Find the general solution of this separable differential equation. dy y cos x dx sin x + 2

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Q: 5. Find the general solution for the differential equation -(sin y + y sinx )dx + (cos x – x cos…

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Q: Solve the differential equation 2 ď²y dy + 4y = cos(ln x)+x sin(ln x), r > 0, dr dr? by using the…

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Q: Find the differential equation of the family of cardioids r= a(1+cos 0).

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Q: dy +ky = a sin bx dx %3D Show that the solution of the differential equation is given by: 2 +b²+ab K…

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Q: Given the differential equation: D'(sin x- cos x+3e" +x) What is the second derivative? a - sin…

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Q: Find the value of k so that the differential equation (6ry³ + cos y) dr + (2kz²y² – 1 sin y) dy = 0…

A: we have to find the value of k when the given equation is exact            (6xy3 +cosy)dx…

Q: State the order of the given ordinary differential equation. (sin 8)y"" - (cos 8)y' = 7 Determine…

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Q: Find the solution of the Differential Equation: dx/dt=cos x cos^2 t

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Q: sin x sin y y' cos x cos y

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Q: dy +(cos x)y = sin²(x) using first order linear differential equation. dx Solve (sin x) %3D

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Q: 1. A solution for the differential equation is y = e"x A, sin (vx) + A, cos (vx), where m and n are…

A: Let's find.

Q: What is the general solution to the differential equation sin y (x + sin y)dx + 2x² cos y dy = 0 ?…

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Q: Particular Integral for the differential equation ( D +D+4)y =sin2x is given by cos2x a. O b. cos2x…

A: By the using rule of particular Integral we can find integral

Q: Given: (1+ 2ytan x)dx - dy - 0, determine the solution to the differential equation. O a. 2y cosx-…

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Q: sin x sin y dx + cos x cos y dy = 0 %3D

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Q: State the order of the given ordinary differential equation. (sin 0)y"' – (cos 0)y' = 8 %3D…

A: NOTE: Refresh your page if you can't see any equations. . The order of the highest derivative term…

Q: For an exact equation, Show that this differential equation cos(x+ y)dx= (3y² +2y+ cos(x+ y))cdy = 0…

A: We  are given the differential equation : cos (x+y)dx+(3y2+2y+cos(x+y))dy=0 On comparing with :…

Q: The integrating factor for the differential equation dy X- dx 4x cos(x)y = –5e* is e-4 sin(x) Select…

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Q: If the function y = A sin z + B cos a satisfies the differential equation y" + y – 2y = sin z for…

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Q: Find the differential equation by eliminating the arbitrary constant/s. Gedr cos x + Cge y = c1e 3x…

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Q: The differential equation formed by eliminating arbitrary constants a and b of a sin x + b Y = 9 is…

A: We will differentiate the  y twice to get desired differential equation

Q: Solve the given differential equation by separation of variables. csc(y) dx + sec²(x) dy = 0 s(x):…

A: To solve the given differential equation using separation of variables

Q: Given the differential equation: D°(sin x-cosx+3e* +x) 1. What is the second derivative? a - sin…

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Q: The study of undamped oscillations under the influence of an external force F(t) =F0 cos(ωt) leads…

A: Solution:

Q: Find the value of k so that the given differential equation is exact. (7xy³ + cos(y)) dx + (2kx²y² -…

A: Given

Q: )Show that given differential equation is exact hence solve it (cos a sin a - xy²) dx + y(1 – x²)dy…

A: We know that the differential equation  Mdx+Ndy=0 is exact if ∂M∂y=∂N∂x Given differential equation…

Q: 2 sin²2t dx = cos x (1 + cos 2x) dt

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Q: The differential equation formed by eliminating arbitrary constants a and b of y = 8 a sin æ + b is…

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Q: 34. cos x dx + (1 + + - sin x dy = 0

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Q: Find the value of n that makes the differential equation xn (3x+4y)dx +(2xn+1 +2y)dy = 0 exact.…

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Q: Using the substitutions 2 = In y and dz= - dy , the differential equation xtan x + In y)dx +tan x…

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Q: To find the differential equation of y= c,e 2x c e“ cos 3x + c,e“ sin 3x, we use elimination of…

A: First simplify first derivative equation and then derivative it again with respect to x

Q: Verify that the given differential equation is not exact. (-xy sin(x) + 2y cos(x)) dx + 2x cos(x) dy…

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Q: 4. Using the substitution x = cos 0, show that the following differential equation d?y dy sin 0 ·+…

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Q: Solve the exact differential equation (n y - y sin x -без)dx+(, + cos x + 5 seс y tan y - 6у)dy %3D…

A: Here we have to solve the given exact differential equation.…

Q: 5. a) Determine whether the given differential equation is exact. (sin. x)" dy 1+cos y = 0. dx

A: Given: sinxdydx+1+2xcosy=0

Q: Given the differential equation: D'(sin x- cos x+ 3e +x) What is the second derivative? – sin…

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Q: x (1 – sin(y)) dy = (cos(x) – cos(y) – y) dx

A: The differential equation Mdx+Ndy=0 is said to be exact, if ∂M∂y=∂N∂x The solution is: ∫Mdx+∫Term in…

Q: Solve the first order differential equation to find the particular solution. (cos x) + y sin x = 2x…

A: To solve the given differential equation.

Q: Find the general solution of the given differential equation. cos2(x) sin(x)(dx/dy) + (cos3(x))y = 1

A: Given differential equation:                 cos2(x) sin(x) dydx + cos3(x) y = 1         ... (1)

Q: A Bernoulli differential equation is one of the form dy dx + P(x)y= Q(x)y". bserve that, if n = 0 or…

A: y'-9xy=y4x17 divide by y4 y'y4-9xy3=1x17

Q: Find the differential equation by eliminating the arbitrary constant/s. e COsX = c(1 – cos y) %3D

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Q: Use separation of variables to find the general implicit solution to the differential equation. 4…

A: Given that:  4dydθ = ey sin2θy sec(θ) So, by using variable separable, we getyey dy = 14. sin2θ…

Q: What is the general solution to the differential equation (tan x)dy – (4y In y – y tan³x)sec²x dx =…

A: We will convert given differential equation into linear differential equation by appropriate…