The complementary function(C.F.) of the differential equation (D – 7)²(D + 5)y = 7x is O (c1 + c2x)e-* + c3e° + C3e¯ - 5x O (c1 + c2x)e" + c3e¬5æ -5x o (c1 + c2x)e'a + c3e5¤ O (c1 + c2x)e-7® + C3e5æ

Q: Verify that the indicated function y = g(x) is an explicit solution of the given first-order…

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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: The type of the partial differential equation du 2- ởu o'u =0 is +6- +3

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Q: Find the solution of the differential equation (D° + 8D³ + 16D)y = 0 у %3D С, + (С, + C;x)сos y = C,…

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

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Q: The differential equation obtained by eliminating the arbitrary constants A and B from the relation…

A: Please see the answer in step 2

Q: The second-order linear differential equation xy" + 2y' 12x can be solved by first making the…

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Q: Q3/ Choose two only a. if y - asin3x + bcos3x satisfies the differential equation + 4 + 3y =…

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Q: Give the general solution of the differential equation -5x y"+ 10y'+ 25 y =3xe a) O y=C, e*+ C,xe…

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Q: Which of the following is the solution to the differential equation dydx=y2−(xy)2dydx=y2−(xy)2 with…

A: Explanation and solutions is given below....

Q: Differ Equestion EXPERT  NEEDED

A: From the given information, the second - order differential equation is

Q: 29. Verify that the piecewise-defined function 1-x², x<0 x ≥ 0 is a solution of the differential…

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

A: Given: cos2y-3x2y2dx+cos2y-2xsin2y-2x3ydy=0

Q: Form the differential equation for the function 2xy asin2x-bcos2x O a xy" -2y = -4y Ob.xy" + 2y=…

A: Using the product rule of differentiation it can be written that ddx(xy)=y+xdydx . The derivative of…

Q: Solve the differential equation (2x + y) dx - O a. 5x+10y + In |10x O b. O c. 5x O d. 5x (4x + 2y -…

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Q: The general solution of the differential equation x²y" - 2y = Inx is O c,x? + c2xl + 2 lnx - 1…

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Q: Determine the solution of the differential equation 2y"-3y' + 4y = 0 3x V23 y = e (C, cos x+ C2sinx)…

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Q: Let us consider a continuous-time system represented by the following differential equation : 5+ 3a…

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Q: Two linearly independent solutions of the differential equation y" - 6y' + 25y = 0 are O yn = e3x,…

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Q: Find the solution of the differential equation y" – 3y' + 2y = 2x3 – 9x² + 6x %3D a. y = C,ex +…

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Q: Solve the differential equation dy dx 3y3 1 %3D By the method of separating the variables y = x³ y =…

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Q: Verify that the indicated function y = Q(x) is an explicit solution of the given first-order…

A: Solution : when y=125-x2y'=-125-x22×-2xy'=2x25-x22y'=2xy2thus in terms of x,2xy2=dydx

Q: Determine the solution of the differential equation ex y" – 2y' + y = 1+x2 - y = C,e* + C2xe* +÷e*…

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Q: Determine the total solution of the differential equation (D2+5D+6)y=6e(-3x)-100e2x O A. y =…

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Q: The solution of the differential equation 7+ x² + x²y+ 7y 1+ Y dy using variable dx separable x2 Py…

A: Separate the variables from terms of right hand side then transfer the terms of y to the side of dy…

Q: A general solution of the differential equation - 3+4 = 0 is 1. A. y = c,e* +cze2x + c3xe²x B. y =…

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Q: Solve the second order differential equation ý + ý - 6y = 8e* + 3x A:y = ce2x + cze-3x + 2e* + %3D 2…

A: To solve the given differential equation, first we find complementary function (C.F.) and particular…

Q: - Find the solution of the partial differential equation Z, = 6x + y

A: Given : Zxy  = 6x2 + y    Now we Find the solution of the partial differential equation .

Q: Verify that y1(x) =cos2x and y2(x) =3(1−2sin2 x) are solutions to the differential equation y′′+4y =…

A: Given : the differential equation is, y''+4y=0  and two function defined as, y1x=cos2x  and…

Q: Form the differential equation for the function 2xy= asin2x -bcos2x O a. xy" +2y' = – 4xy O b. xy"…

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Q: Show that y = Vx],(Ax), 1> 0 is the solution of the differential equation %3D x*y" + (x²x² – v² +±)…

A: The given differential equation is,  x2y''x+λ2x2-v2+14yx=0 This differential equation can be written…

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

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Q: Determine the solution of the differential equation 2y"-3y'+ 4y = 0 %3D 3X V23 V23 y = e (C, cos x+…

A: Let's find.

Q: What is the auxiliary equation associated with the second order linear differential equation d^2x…

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Q: Form the differential equation for the function 2x-y-asin(2x-b) O a. y"+y=x O b. y" +8y = 4x O…

A: Given, 2x-y=asin(2x-b)

Q: Determine the total solution of the differential equation (D²+8D+16)y = 64cos4x. OA.y = C₁e(-4x) +…

A:

Q: To reduce the differential equation with linear coefficients (X+2y-4)dx - (2x+y-5)dy=D0 to a DE with…

A: We are going to solve

Q: What is the auxiliary equation associated with the second order linear differential equationd^2x…

A: We need to find auxiliary equation.

Q: What is the general solution to the the differential equationy'''=0? A y=C₁+C₁₂x 1 By=C₁+C₁₂x+C₁₂x²…

A:

Q: Verify that the indicated function y = p(x) is an explicit solution of the given first-order…

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Q: The general solution of the differential equation x²y" – 2y = Inx - is O C1x² + c2x¯+ In x 1 4 -2x…

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

A:

Q: The general solution of the differential equation x²y" – 2y = Inx² is C1x=² + c2x – ln x – , O C1x²…

A: The solution is given as

Q: . The standard form of the first order linear differential equation x y'+xy +2 = 0 is,

A: This question is based on to form a standard first order differential equation.

Q: A. Obtain the differential equation of the gi- (1) 3x² – xy² = c (2) y = a cos(x +B) (3) y = c,e¬2x…

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Q: The differential equation formed by eliminating arbitrary constants a ,b and c: y= ax³ + bx+ cx +7…

A: y = ax³ + bx + cx + 7 So, y' = 3ax² + b + c  So, y" = 6ax  So, y''' = 6a

Q: Form the differential equation for the function 2x-y = asin(2x - b) O a. y" + 4y = 8x O b. y" +y = x…

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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: Determine the solutions of the 1st-order linear differential equations below: (a) (x +3y)− x y′ = 0

A: Explanation of the answer is as follows

Q: Verify that the indicated relation is an implicit solution of the given first order differential…

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.