Solve the following IVP: (2ry² + 3y sin z + 2y)dx + (3r²y – 6 cos I + 4r)dy = 0, y(0) = –1.

Q: 3. Solve: cos xdx + ( 1+ | sin ædy = 0 %3D

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Q: Find a particular solution to y" + 16y = -16 sin(4t). Yp ||

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Q: Solve the following exact equations: 1) (сos 2y — 3x*y*dx + (сos2y — 2xsin 2y -2x'y)dy %3Dо 2) (2ху-…

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Q: Determine the particular solution to dy/dx= 2 sin x, y(pi)=-2

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Q: Q1) Solve 1 + cos y – 2xy) dx – (xsin y + x²)dy = 0 +1

A: Given differential equation is  1x2+1+cosy-2xydx-xsiny+x2dy=0 This equation can be written as…

Q: Find the solution of the IVP: y" – 9y = sin 2t, y(0) = 0, y'(0) = 1 using method of undetermined…

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Q: Find the general solution of the equation d2y/dx2 - 2dy/dx +4y =2e sin2(x/2)

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Q: cos²x sinx dy + (y cos³x - 1)dx = 0

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Q: Find the solution of y" + 3y = 126 sin(3t) + 54 cos(3t) with y(0) = 2 and y' (0) = 7.

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Q: If y = (3x)sin (2æ) then %3D dy dx (Be sure to express your answer in terms of x)

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Q: Solve the following 1 √√1-3x siny Cos 2y +1 cb₁ x² y² + x³ In x = 1 - 3 xy (a) - dx + dy = 0

A: We have to solve the differential equations given as follows a) 1sin ydx+1-3xcos 2y+1dy=0b)…

Q: Find the General and Particular solution of = 8 sin 4x ; y = 6 when x = 0 %3D dx

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: Solve the IVP (1/x + 2y^2x)dx + (2yx^2 - cos(y))dy = 0, y(1) = pi. Give an implicit solution.

A: Consider the differential equation 1x+2y2xdx+2yx2−cosydy=0.........(1) Compare the equation (1) with…

Q: *10. cos Z = 0.5234 YX _ y 24

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Q: Find a particular solution to y" +4y = - 12 sin(2t).

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Q: cos²x sinx dy + (y cos³x − 2)dx = 0

A: Given problem:- cos2(x) sin(x) dy+(ycos3(x) -2) dx=0

Q: SV1- x2 sin-1x dx

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Q: Find the solution of the equation M a²z a²z = e cos y Əх² ду? which tends to zero as x→∞ and has the…

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Q: FIND Y(s) OF THE GIVEN EQUATION. y" + 4y = cos(t-3)+4t, y" - 6y + 15y = 2 sin(3t), y(3)=0_y' (3)=7 y…

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Q: Show that the following equation is exact and find its general solution. (3x²y+ 4y + dx + (x + 4x +…

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Q: Find the complete solution of ey sin x dy cos²x = 0 dx

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Q: 4. Find a general solution to the equation y' – 3y = e" sin(2x). -

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Q: 2:Solve: cos (x+ y) dy = dx %3D

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Q: S cos³y sin³y dy 3.

A: Given,            ∫cos3ysin3ydy

Q: Solve the following equations  by the method of undeterminedcoefficients. y" + y = cos 3x

A: To solve the given equation by the method of undetermined coefficients y''+y=cos3x

Q: Solve the given higher order DE y" – y" + 3Dy – 5y = e*Sin 2x

A: Auxiliary equation corresponding to given differential equation: m3-m2+3m-5=0 Roots of polynomial…

Q: dt 1. cos (2 sin 2r) V1-4r

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Q: Find a particular solution to y" + 16y = 16 sin(4t). Yp

A: The given differential equation is:y''+16y=16sin4t        ...............(1)The auxiliary equation…

Q: cos 2y dy sin y

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Q: Solve the following IVP: (3y cos x + 2xy^2)dx + (4y + 9 sin x + 4x^2y)dy = 0,  y(0) = 1.

A: The given Initial value problem is of the form M dx+N dy=0. After finding ∂M∂y, and ∂N∂x, we see…

Q: Find the general solution to the DE using the method of Undetermined Coefficients: y" + 9y = 2…

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Q: -x2 + 5 2. y = cos 2x³

A: Given: y=-x2+5cos2x3

Q: with y (0) = 7 and y' (0) = 2. y" + 9y' = 162 sin(9t) + 648 cos(9t) y =

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Q: Find the solution of d2y/dx2 +4y=sin3xx+cos2x

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Q: у" + 4y' + Зу %3D sin (e*)

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Q: y" + 3y' + 2y = cos4x %3D

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: 2y dy = sin dx when y(1) 4 + %3D -

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Q: 7. y" + y = 3 sin(2r) +t cos(2t)

A: The general solution of an ordinary differential equation of the form;…

Q: Solve by Bernoulli's Equation 2. sin y(x + siny)dx + 2x?cos y dy =0

A: We find the solution by Bernoulli’s Equation.

Q: 211 2E1 sin nx dx = cos nx dx 0, where n integer.

A: To show that ∫02πsin nx dx= ∫02πcos nx dx=0 Where n is integer.

Q: Find a particular solution by inspection of d²y dx2 +y = -7+e* + cos 2x – 10 sin x

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Solve the following Bernoulli's equation by using an appropriate substitution. sin y (x + sin y)dx +…

A: We have to solve the give Bernoulli's equation by substitution.

Q: 8. (sin°(5y)dy

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Q: Use any appropriate method to find the general solution of each of the following equations. dy sin 2…

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Q: 3.) Solve the equation using discontinuous function: y" + 9y = cos(2t) – U37(t)cos(2t) , y(0) = 0,…

A: We will find out the required solution.

Q: Find a/dx2 at the given point without eliminating the parameter. *=0+ cos0 and y =1+sin ; 0 =n/6

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Q: Solve the given DE: (yexy + cosx)dx + (xe*y)dy = 0.

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Q: Find the solution of d2y/dx2+4y=sin3x+cos2x

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Q: Solve the following a) 2d²y_dy 3y = 25 sin 2x dx² dx d²y b) - 4 - 3y = 25 sin 2x dx² dx c) d²y dx² +…

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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.