Find the general solution of 2ey cos 2x dx + (ey sin 2x + 3y sec2 y2)dy = 0. a. e sin 2x +y tan y? = C %3D b. ey sin 2x +tan y2 = C %3D c. e cos 2x + y tan y² = C d. ey cos 2x + 3y tan y? = C

Q: Solve the given initial value problem: sin(2x) dx + cos(3y)dy = 0, y (Do not need to solve for y.)

A: We have to solve the given initial value problem…

Q: Consider the following IVP: y" +y' = -cos x; y(0) = a, y'(0) = b Find the general solution. A y(x) =…

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Q: If y = 12y sin(4z) – 12z sin(4y), then (z, y) = 6y? sin(4z) + 3z cos(4y) + h(x) O (z, y) = 6y²…

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Q: 2. Let y(x) = tan r. Show that y is the solution to the initial-value problem %3D dy =1+ y, y(0) =…

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Q: Determine the solution of an initial value problem; 2e°cos2x dx+ (e'sin2x + 3y sec²y²) dy=0, =0 4 A…

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Q: Is the ODE (sin(x-y)+1)dx=(sin(x-y)-2y)dy satisfied by the implicit solution x+y2=cos(x-y). Show…

A: An implicit function, however, is an equation that defines a relationship between two or more…

Q: Find dy/dt. y (1 + sin 10t)-3 Select one: A. -3(1 + sin 10t)* B. -30(1 + sin 10t)¯“ cos 10t C.…

A: The solution is given below in the next step:

Q: 1) Solve the IVP: y" + 2y' + 2y = 5 sin t + 5 cos t : y(0) = 1 and y'(0) = 2

A: Given initial value problem is  y''+2y'+2y=5sint+5cost, y(0)=1, y'(0)=2. Let y'=dydt=Dy and…

Q: The two parameter family of solutions of the DE: y" + 25y = 0 is y = c1 sin 5x + c2 cos 5x. Then,…

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Q: The solution to the initial value problem, y" + 4y' + 5y = cos cos 9x, y (0) = 0 is y (x) = ? ye(e,…

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Q: The solution of the nonhomogeneous DE y" + y = sec?x is O None of these y = c1cosx + c2sinx +…

A: The given DE is, of the second-order and it is y''+y=sec2x which is non-homogeneous DE. So, first we…

Q: Find the particular solution : y" + y' + 16y = cos4x (a) yp = -4sin4x Yp =sin4x (b) %3D %3D (c) yp =…

A: The correct option is b i.e. yp=14sin4x i.e. 14sin4x is the particular solution of the differential…

Q: 3- The integration of ſ cos(7x + 5).dx is: (a) cos(7x + 5) + C (b) sin(7x + 5) + C (e)극 sin(7x + 5)…

A: The given integral is, I=∫cos7x+5dx Now, substitute z=7x+5in the above integral,…

Q: Solve the initial value problem. (tan (2y) - 5)dx+ 2x sec (2y)+ y (2y)+dy=0, y(0) =1

A: Here we have to solve given initial value problem,

Q: Suppose that ye cos Bx is a solution of y-y +ay -9y =0 where a and B are real constants Then the…

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Q: 8 12. If y = then what is %? dx Vx+4' dy а. 4x(x + 4) dy С. dx = -4Vx + 8 %3D dx 3 dy b. dx -4(x +…

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Q: Which of the following functions is a solution of dx 12x – 8y dt dy 16x – 4y dt O a. æ(t) = et…

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Q: Find the solution to the Bernoulli equation. y = 2(3x+ y)2 – 1; x= 0,y=1 O 4tan-1(3x+ y) = 8x + T…

A: The solution is given as

Q: Given, y = (1+ cos 2t)-Find dy dt 8 sin 2t (1+cos 2t) sin 2t 5 (1+cos 2t) -4 sin 2t 5 (1+cos 2t) 8…

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Q: Solve by Bernoulli's Equation 1. (3x - 2y + 1)dx + (3x – 2y + 3)dy =0 ANS. 5(x + y + c) = 2ln |1 2.…

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Q: Find the solution of the given initial value problem in explicit form. π sin(2x) dx + cos(9y) dy =…

A: Given: Now,                sin(2x)dx+cos(9y)dy=0Integrating both sides we…

Q: Find the General Solution: (show solution) 1.(x3+xy2-y)dx –(x-x2y-y3)dy=0   Ans: (x2+y2)2-4xy+C=0

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Q: Solve the initial value problem. dy = -8 eX dx tan e sec e y(0) = 8 sec 1+ 4 y = 8 sec eX+ 4 y = -8…

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Q: Solve the initial value problem: dy 2xy ) = y (y + sin æ); у (0) — 1 + cos x 1+y? dr

A: The given differential equation is: 11+y2+cos x-2xydydx=yy+sin x ;          y(0)=1

Q: Match the following guess solutions yp for the method of undetermined coefficients with the…

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Q: 2. If y = C₁ cos2x+C₂ sin 2x+2sin x is the general solution of a certain nonhomogeneous LDE, which…

A: The given general solution of non-homogeenous  LDE.  y= c1cos2x +c2sin2x +2sinx   We have to find…

Q: Find the solution to the initial-value problem. dy dx = y2ex sin(7x), y(0) = 1

A: Given:    dydx = y2exsin(7x)       ,   y(0) =1

Q: 6. Find the general solution of (cos cos y + ycos x ) dx + (sin sin x x cos y - y sin x = C - x cos…

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Q: Find the solution to the initial value problem y (z) – 6 ( y (x) ) + 10 y (x) =-2 sin (3 z) + 36 cos…

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Q: Find the general solution of the d dy 2c-2v = dx 3 sin(x/2)√ √cos³(x/2)

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Q: Solve the IVP. Give implicit solution dy 7 cos(x)(e®v – 9ye). 6e" sin(2æ); y(0) = 0 dx

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Q: The general solution of y" + 16y3 cost is: Select one: a. y= C, cos(4t) + C2 sin(4t) + 1 -tcost 15 O…

A: Using Solution of Linear Differential Equation

Q: Find the solution to the initial-value problem. dy dx = y2ex sin(2x), y(0) = 1 y =

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Q: If z = x2 – y2 and x t cos 2r and y = r sin t, then %3D a2z is ar2 (A) 2 cos (2r) + 2r? cos?(t) –…

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Q: Verify that y = 7 sin 2x + 9 cos 2x is a solution of y" + 4y = 0 %3D

A: Given, y = 7sin2x +9cos2x  We have to verify y = 7sin2x +9cos2x is a solution of y"+4y = 0

Q: your final answer 2. 54-e) cos(-+ In z) dz 3. Setanx+(tan² x)e+tanx dx S 4. 22x cos²x-ain 2x dx 5.…

A: I am attaching image so that you understand each and every step.

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

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

Q: Find the solution of the given initial value problem in explicit form. sin(2r) dr + cos(5y) dy = 0,…

A: Find your answer below

Q: Differential Equation Activity

A: To find the general solution of the given differential equation

Q: 6. Find the general solution of (cos cos y +ycos x) dx+ (sinsin x – x sin sin y ) dy = 0 A. x cos y…

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Q: If u(x, t) = E1 fn(t) sin(nx) is the solution Utt – 9uzz = 2e2t sin(3x) + e-2t sin(4x) m=1 u(0, t) :…

A: Given: ux,t=∑n=1∞fntsinnx is the solution of the PDE…

Q: Find the general solution of the nonhomogeneous equation y " - 3 y "+4 y ' – 12y =e + 2 1 3* + C,…

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Q: Determine the solution of an initial value problem; 2e'cos2r dx + (e'sin2r+3y sec?y²) dy=0_y 0= (A…

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Q: Show that an implicit solution of 2x sin?(y) dx - (x2 + 17) cos(y) dy = 0 is given by In(x? + 17) +…

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Q: Find the general solution of the DE: dy/dx = sin(7x) cos(5x) + cos(7x) sin(5x).

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Q: Consider the D.E. y(4) + 4y" = 1 – cos(2æ). Then a suitable form of the particular solution can be…

A: Let us consider the  differential equation F(D) y=Q(x) then the particular solution is obtained by…

Q: 8. Which of the following is the solution of * [2x + ycos(xy)]dx + xcos(xy)dy = 0 x? + cos(xy) =c x?…

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Q: Determine the solution of an initial value problem; 2e cos2x dx + (e'sin2x+3y sec?y2) dy=0 y =0…

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Q: Find the solution to the initial-value problem. dy dx = y2ex sin(7x), y(0) = 1 y

A: We will solve the given differential equation as shown below