The complementary function(C.F.) of the differential equation (D + 6D+ 18)y-zis O (e +ez)e * O "(e cos 3z - o sin 3z) O (e cos 3z + o sin 3z) O e"(e cos 3z + eg sin 32)

Q: A differential equation of first order and first degree is homogeneous if ans. None of these dy dx =…

A: We want to find true option.

Q: Verify that the function y = 6x − 4 sin x + 1 is a particular solution of the differential equation…

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Q: State the order of the given ordinary differential equation. (2x - tan(17x))y"" - x²y" + 18y' =…

A: Given the ordinary differential equation is  2x-tan17xy'''-x2y''+18y'=18sinhx+16

Q: (1) Determine whether or not the function u(t) = sin(2t) + cos(2t) is a solution to the differential…

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Q: Verify that the given function y = sin (x2 + C ) is a solution of the given differential equation:…

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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: Which of the following is the Euler (Cauchy) differential equation whose general solution is y =…

A: In this question, the general solution of the Cauchy  equation y=c1cos(lnx)+c2sin(lnx) It is…

Q: What is the simplest form of the integrating factor for the differential equation y' +…

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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: Find the value of a and b for which the given differential equation is exact: *siny + (a - 3)ysinx)…

A: Equation is exact for the values a= 5 and b= -1 Therefore option C is correct

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: Obtain the differential equation whose general solution is y =a sin 6x- bcos 6z, where a and b are

A: Given: y=asin6x-bcos6x for finding differential equation for given equation, we have to eliminate a…

Q: This nonlinear differential equation, which describes wave mo- tion on shallow water surfaces, is…

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Q: y" – 2y – 3y = 2e² – 10 sin z

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Q: Find the solution to the differential equation that satisfies the given initial condit dy dx I sin x…

A: Topic:- differential equations

Q: Use Frobenius method to find the first three non-zero terms for the following differential equation:…

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Q: Consider the differential equation dy (t – 81) + 5ty = sin(t) with y(1) = 2t. %3D There exists a…

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Q: The equation, sin y-2 sin(2) sin(2y) y+ cos z + 2acos () cos(2y) = 0 is an exact differential…

A: We have to solve

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: (4r + 5)2 2- + tanzy= dr COSI

A:

Q: Find the differential equation that corresponds to the following solution. Give your answer both in…

A: The given solution is: y=C1 sin(4x)+C2 cos(4x)+C3 x sin(4x)+C4 x cos(4x)

Q: The Particular integral of the differential equation (Dª – 36)y = cos 6x is PI = cos 6x 1260 PI = z…

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Q: Show that the functions x, x2, form an FSS for the differential equation x³y" +x2y" - 2xy' +2y = 0.…

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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: Convert the differential equation d²y - 3y + 2y = 4 sin x dx² dx with the initial conditions y(0) =…

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Q: Suppose a solution to a differential equation is given by: x(t)=5cos(2t)+12sin(2t) (a) Express the…

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Q: Find the solution of these differential equations : 1. dx %3D ху — у sin x dy 2. 1+v dx = cos x cOS…

A: Given that  The following differential equations  To find out the solution of the differential…

Q: The particular integral(P.I.) of the differential equation (D² + 5²)y = 2 cos² x – 1 is_ cos2x 29…

A: Here we use the trigonometric properties. Also use the method of undetermined coefficients to solve…

Q: The Pl of differential equation (D +D+1)y = cosx is a) sin 2x b) sin x 1 cos 2x 1 sin 2x 3 c) d)

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Q: The particular integral of the differential equation (D² + 2) (D + 4)y = 2 + sin² x + cos² æ is_ 8

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Q: The particular integral of the differential equation (D² + 2)(D+3)y=2+sin² x + cos? æ is 6

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Q: The degree of the differential equation dx (割()). +sin dy +1=0is: dx dx Select one: O A. 2 О в. О O…

A: Degree of a differential equation: Order of a differential equation is the order of the highest…

Q: Find the differential equation of a family of circles, each having its center on the line y=z and…

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Q: The degree of the differential equation 2 (d²y' (dy\ 3 +1 = 0 dx2 dx, none O not defined O 2

A: Degree of the differential equation is the power to which the highest order derivative is raised.

Q: Show that the function y=ex(sin2x+cos2x) is a solution of the differential equationy′′−2y′+5y=0.

A: We find the first two derivatives of y using the product rule

Q: Find the solution to the differential equation that satisfies the stated condition. sin (5x + T),…

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Q: y tan x dx – In cos x dy = 0

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Q: Find the differential equation such that y(x) = (x + 10)°(c,cos(2ln(x+ 10)) +c,sin(2ln(x+ 10))) d²y…

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Q: The Particular Integral of the differential equation (D² + 4)y = 3 sin 2x is || PI = 3 cos 2x 8 PI =…

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Q: Solve this first order differential equation dy, 2 +y = -x²y? cos x

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Q: The particular integral(P.I.) of the differential equation (D² + 9²)y = 2 cos² x – 1 is_ cos2x 77…

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Q: The Particular Integral of the differential equation (D² – 9)y = 6 cos 3x is PI = 6 sin 3x 18 O PI =…

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Q: A (플) n (2프) %3D Cos dt?

A: This is the problem of differential equation.

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

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.