What differential equation has y = x² cos y- 4x + C as a solution? a. (2x cos y – 4)dy – (1+ x² sin y)dx = 0 b. (2x cos y- 4)dx + (1 + x² sin y)dy 0 c. (4 - 2x cos y)dy- (1+x² sin y)dx 0 d. (4- 2x cos y)dx + (1 + x sin y)dy = 0 e. None of the above

Q: The differential equation for which sin¬ x + sin¯ y = C is given by V1- x²dx + /1- y² dy = 0 b. V1-…

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Q: Q2:- Check that the indicated functions are solutions to the given differential equation :- 1) y" +…

A: Kindly go through the solution and let me know in case of any doubt or further clarification in the…

Q: I. SOLVE the following DIFFERENTIAL EQUATIONS. 1. cos'x sin x dy + (y cos³x – 1) dx = 0 2. xy' =2xex…

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Q: The solution of the differential equation 5/1 – x2 ? dy dx 7/1 - y? = 0 is - 5 sin-x – 7 sin-y = C 5…

A: Question is solved.

Q: Which one of the following equation is exact differential equation a) (y sin 2x)dx-(y² +cos? x)dy =…

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Q: The differential equation formed by eliminating A and B from y = e-2* (A cos x +B sin x) is A. y2 -…

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Q: 2. Solve the ordinary differential equation. a) e2*cos(y)sin(x)dx + e*tan(y)dy = 0 b) (x* + 1)dx -…

A: To solve the following problem we use the seperation of variable method and also use  standard…

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

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Q: The differential equation of y = 4c sin z after elimination of the arbitrary constant c is O y = 4y…

A: Answer

Q: What is the general solution of the differential equation; y’ = 2x cos (x^2)  a. y = xsin (x2) + C…

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Q: Solve the differential equation e sin 2y dx - 3x-cos 2y dy A - 3ln(sin 2y) = C B +3 In(cos 2y) = C…

A: .

Q: Which differential equation follows the form A (x) dx +B(y) dy=0? ysinxdx-2xcosydy=0 B There is no…

A: Check for all the options.

Q: Solve the exact differential equation (In y - y sin x-6e³x) dx + ( + cos x + 5 sec y tan y - 6y)dy =…

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Q: Solve the following linear differential equations. 1. dx/dy= siny-xcscy 2. dx/dy + (1/x + tanx)y =…

A: As per bartleby guidelines for more than one question asked only one is to be answered please upload…

Q: The general solution of the differential equation d?y + 6y = sin 4x is dx 2 sin 4x O y = c¡ cos /6x…

A: The given differential equation is d2ydx2+6y=sin 4x. Consider the homogeneous part of the given…

Q: Find a suitable form for particular solution of the differential equation y" - 4y' + 13y te"…

A: 1st is correct answer see the solution on step 2

Q: a. (y2-xy)dx + (x2-xy)dy = 0

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

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Q: Solve the exact differential equation (In y -y sin x-6ex)dx +( + cos x + 5 sec y tan y -6y)dy = C y…

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Q: Solve the exact differential equation (In y - y sin x-6e)dx + ( + cos x + 5 sec y tan y - 6y)dy = 0…

A: Given a differential equation, Compare the given differential equation with M dx+ N dy=0 Therefore,…

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: What differential equation has y = x2 cos y - 4x + C as a solution? a. (2x cos y – 4)dy - (1 + x²…

A: The objective is to find the correct differential equation

Q: Verify that y = c, sin 3x + c2 cos 3x + 4e* is a solution to the differential equation y"-y" + 3y'-…

A: We have to verify that, y = c_1 sin 3x + c_2 cos 3x + 4e^x ;  is a solution to the differential…

Q: Which of the following differential equations can be solved by separation of variables? у1+2у)dx -…

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Q: 2. Verify that for constants A, B, C and D the function p(x) = Ae* + Be* + C sinx+ D cos x is a…

A: We have to solve given problem:

Q: Form the differential equation for the function x +2y = a sin3x - bcos3x а. Зу" - 18у %3D -9х O b.…

A: The second order differential equation for a function can be found by differentiating the function…

Q: Solve the differential equation [cos (2y) - 3x²y²] dx + [cos (2y) - 2x sin (2y) — 2x³y] dy = 0 - a.…

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Q: What is the general solution to the differential equation dx 8e4x 2 cos(2y) A 2 sin(2y) – 8e4r = C…

A: topic - differential equations

Q: Solve the differential equation -1 (x + 3)¯¹ cos (y)dx cos (y)dx O a. cos (y) In b. cos (y) In -…

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Q: solve the differential equation: 2xy dy dx x² + y² +1 Select one: y? 1 O a. F(x,y)=x-++c 1 O b.…

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Q: Show that y a solution af y +2xy =0, Show that y = ka solution of y" - 3y' + 2y - 0. (12 sin(3x)…

A: We have to solve the first and second problem, we subtitute the value of y, y', y'' and y''' in the…

Q: B. Determine if the differential equations are exact or not by performing test of exactness. Do not…

A: here we have to check the exactness of the given differential equation.

Q: 10. Find the solution of the differential equation ( D+ 8D° + 16D y = 0 y = C, + (C, + C,x)cos y =…

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Q: Find the solution of the differential equation y' cos x 0. sin x a. y = cos x + C sin x b. y = cos x…

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Q: Using D-operators, the differential equation y"-xy'+ 2y – cos 5x can be written as: A (2D?– xD…

A: Please refer the attached image for complete solution. THANK YOU.

Q: Solve the differential equation: (9 + 2x sin y) dx x? cos y dy = 0 O z sin y = ca – 3 O (E) O z +…

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Q: Obtain the solution to the differential equation: y cos x(2y sin x+ 1)dx+ (sin x- 2y cos²x)dy = 0-…

A: The given differential equation is: y cos(x)2y sin x+1 dx+sin x-2y cos2x dy=0

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: Solve the exact differential equation (In y -y sin x-6e)dx+( + cos x + 5 sec y tan y -6y)dy = 0 y (A…

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Q: Which of the following differential equation can be solved using separation of variables? a.…

A: Topic:- differential equations

Q: To solve the ordinary differential equation dy 4- + 5y? = sin x , y(0) = 5 %3D by Euler's Method,…

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Q: Which of the following is a solution to the given differential equation: y cotxdx + (3 sinx- Sy)dy =…

A: Explanation of the solution is given below....

Q: For the differential equation (2y - x³) dx + 3 x y'dy = 0, what is P (x) and q ( x) ? 2 А р (х) %3D…

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Q: Solve the differential equation sin 2y dx - 3x-cos 2y dy = 0 by separation of variables. (A ex² _…

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Q: Consider the differential equation: y" + y = sec x,0 <x <n/2 What is the particular solution y.? Yp…

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Q: Solve the differential equation. y' + y tan x = cos X, -π/2<x<π/2 A y = x cos x + c cos X, - B) y=x…

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Q: Solve the following differential equations 1. sec3x dt = tan2t dx

A: according to our guidelines we can answer only first question and rest can be reposted.

Q: To solve the ordinary differential equation dy 4 + 5y² = sin x ,y(0) = 5 dx by Euler's Method, you…

A: The given differential equation is       4 dydx+5 y2=sinx,  y0=5.......(i) We have to arrange the…

Q: Solve the exact differential equation (n у - y sin x- бе)ӑx+(3, + cos x + 5 sec y tanу -бу)dy %3D 0…

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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.