Which of the following is a particular solution of the equation y"+y'+7y=4cos2x? O a. 8cos2x/13-12sin2x/13 O b. 8sin2x/13-12cos2x/13 O NS. -8sin2x/13-12cos2x/13 O D. 8sin2x/13+12cos2x/13 O to. 8cos2x/13+12sin2x/13

Q: Find the linear, nonhomogeneous differential equation with constant coefficients whose solution is y…

A: Given solution to a linear non-homogenous differential equation is    yt=c1et+c2e2t-3tet+cost-e-t2…

Q: 11) Determine a function M(x,y) such that the differential equation M(x, y)dx + (12x10y³ – 12æ"y²)dy…

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Q: The differential equationy2y - v3 Y* -o after using substitution y=vx will convert into separable…

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Q: Solve the second order differential equation ÿ + 2y = 3 cos 2x A:y = c, cos(vZx)+c2 sin(vZx)+…

A: General solution to a nonhomogeneous linear differential equation a2(x)y''+a1(x)y'+a0(x)y=r(x) is…

Q: Show that the general solution of y(4) − y = 0 can be written as y=c1cost+c2sint+c3cosht+c4sinht.…

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Q: Show that the y,(2) = K, (1 – 2x* +*-*-)* * (2x -+ 4 x6 + ... 45 4 + K2 (2x 4 8 + ... 3 15 315 is…

A: we have given yh(x)=k11-2x2+23x4-445x6+...+k22x-43x3+415x5-...is complementary solution of…

Q: Verify that the given function y is a solution of the initial value problem that follows it. y(t) =…

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Q: Consider the differential equation d²x dx + b. + cx = 0, dt (9.4.5) di2 where b and c are constants.

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Q: Give the form of a particular solution of -4x yl4) – 256 y =2 e**+3 e+ cos(4 x) – 2 a) O z=Ae -4х +…

A: OPTION D IS CORRECT.

Q: Which of the following is the differential equation of the family of cubics defined by cy^2 = (x -…

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Q: 2. Get the general solution of the differential equation (x + 3y - 5)dx + (x + 3y + 10) dy = 0. (10…

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Q: Which of the following is the particular solution of a nonhomogeneous differential equation…

A: As per the company's guidelines, we are supposed to solve first question for you, kindly repost the…

Q: Determine the solution of the differential equation: dy 2x ly = (x² + 4)cos x with initial condition…

A: the given differential equation is: dydx-2xx2+4y=x2+4cosx the initial condition is: y(1)=0.

Q: Suppose we have the following system of linear differential equations: x' = 2x – 2y y = 2x – 3y. -…

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Q: Solve the second order differential equation y + 2y = 3 cos 2x A:y = c, cos(vZx) + cz sin(vZx) +…

A:

Q: Obtain the solution of the following differential equations. 3. (16x + 5y)dx + (3x + y)dy = 0 ; the…

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Q: The partial differential equation 5x + 8y- = 7+ e10z is elliptic if .......... O 1. x > 0 and y 0 O…

A: We have to choose the correct answer

Q: Show that the family of circles (x+1)2 + (y-1)2 = c2 can be interpreted as two families of solution…

A:

Q: What is the particular solution to the differential equation x(x³ – xy² + 2y³)dy – y(x³ + 2y³)dx = 0…

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Q: 3. Show that the equation (6xy – y*)dr + (4y + 32² – 3ry²)dy = 0 %3D is exact. Hence solve the…

A: Given that  The differential equation is  To solve the differential equation with intial condition

Q: Two linearly independent solutions of the differential equation y" + 2y' + 4y = 0 are Select one: O…

A: We have to find linearly independent solution of given differential equation.

Q: Czsin(2x) + C4cos(2x) y= C¡sin(x)cos(x)+ C2sinh2x+ is the general solution of which of the following…

A: Here, we have the general solution : y=C1sin(x)cos(x) +C2 sinh (2x) +C3 sin(2x)+C4 cos(2x)ex…

Q: Find the solution of the given initial value problem. y" + 4y = u,(t) – uzn (t), y(0) = 7, y' (0) =…

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Q: You can think of the first two cases as being performed in vacuum (no friction) and air of water…

A: Let's find.

Q: Use the method of undetermined coefficients to solve the initial value problem. y" + 4y = + 10e',…

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Q: The solution of the differential equation + 25y 0 is dy Oy= Acos25x + Bsin25 O y (Ar + B)e 5 O y=…

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Q: find a particular solution yp of the given equation. primes denote derivatives with respect to x.…

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Q: Find the linear, nonhomogeneous differential equation with constant coefficients whose solution is y…

A:

Q: Match the differential equation with it's particular solution form. | y’’ – 6y' + 9y а. Ate 2t |y'’…

A: We have to match the following differential equation with it's particular solution form.

Q: Which of the following systems is equivalent to the differential equation y" + 9y" = cos(x) – y? 9uz…

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Q: What is the solution of the differential equation y" – 8y' + 25y = 36e* -4x -4x y = Cje* cos3x +…

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Q: Find the general solution for the system of differential equations. x' = -3x – 2y y' = 2x + y Use…

A: Consider the given differential equation.

Q: If the auxiliary equation associated with a homogeneous linear differential equation with constant…

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Q: The auxiliary equation of the differential equation 4y" – y" – 7y = 0 is: None of them…

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Q: y=Aexp(Bx)+Fexp(Gx) is the particular solution of the second order linear differential equation:…

A:

Q: Write the following first-order differential equations in standard form. dy x*y + cos(7x) dx

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Q: What is the solution of the differential equation y" – 8y + 25y = 36e4x ? -4x O y = C1e¬4 cos3x +…

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Q: A student is solving a Cauchy-Euler differential equation and obtains the following solutions of the…

A: Use the cauchy Euler method to solve this problem.

Q: Two linearly independent solutions of the differential equation y" + 2y' + 4y = 0 are Select one: O…

A:

Q: Solve the given differential equation (2x – y + 2) dx + (6x – 3y+1) dy = 0 O 91z – 21y – 5 ln(14x –…

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Q: Solve the second order differential equation ÿ + ỷ – 6y = 8e* + 3x 1 A:y = ce2x + c2e-3x + 2e* + 12…

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Q: Compute the general solution valid near the origin ((+4x² )y" - By = O 'y= s{1 - 4x°) + a»\x=…

A:

Q: Given the differential equation 4ry + 6x) dr + (r³ – 6x²y² – 1) dy = 0 ,What is (3z y 6M by %3D -- O…

A: Given:       3x2y-4xy3+6xdx+x3-6x2y2-1dy=0 Here M=3x2y-4xy3+6x            N=x3-6x2y2-1

Q: Solve the differential equation y' – 3y = 4et at y(0) = 6. O y = 4e3t – 2e5t %3D | O y = 4e¬3t +…

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Q: Find the roots of the following differential equations and match with their complete solution.…

A: We are given differential equations and we need to match them with the solution given in the right…

Q: Show that xand x-³are solutions to the higher order differential equation x?y" + xy' – 9y = 0 with…

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Q: Find a differential equation for y=c1e^9t +c2e^-4t. Oy"+5y'+16y=0 Oy"-5y'-16y=0 Oy"+5y'+36y=0…

A: Find DE

Q: Two linearly independent solutions of the differential equation y" +2y+4y 0 are Select one: Y1 = e…

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.