Find the solution of the differential equation у" — 16у 3D 2е\x y = C,eªx C2e¬4x + +xe4x а. 4 b. y = C¸e4x C2e¬4x xe4x 4 %3D с. y = C,e4* C2e¯4x + xe4x 2 d. 1 y = Ce4x C2e¬4X – xe4x 2

Q: According to the differential equation: T'=0.1T(1-T/1000)-0.05T What are the equilibrium values and…

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Q: The solution of the differential equation 3.9 + x² + x²y+ 3.9y 1+ Y dy dx using variable separable y…

A: The given equation is dydx=3.9+x2+x2y+3.9y1+y On simplifying this, we get…

Q: show that y2 = Cx + (1/8) C3   is a solution to the differential equation y= 2xy' + y2 (y')3

A: y2=Cx+C38and given ODE is:y=2xy'+y2(y')3

Q: 6) ( y - 2xy ) dx + 3x'dy - 0 ; y( 2) = -1

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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: y"' – 2y" + y' = te' + 5 , with y(0) = 2 ;y'(0) = 2 ;y"(0) = -1 %3D %3D

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Q: Find the gene solution of the differential equation y+2xyy'-e-2yy'=0

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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: 8. Find the solution of the differential equation (D4 – 2D3 + D2)y = 0 y = Ci + C2x + ex(C3 + y = C1…

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Q: determine two linearly independent solutions to the given differential equation on (0,∞). Q.…

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Q: Determine the appropriate form for yp on the differential equation y"=9x^2 + 2x -1 a. y=Ax^4…

A: given the differential equation :

Q: What is the general solution to the differential equation 2 dt S - - - 5t3s3 ? t = s²(C – t*) t =…

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Q: Find three linearly independent solutions of the given third-order differential equation and write a…

A: The characteristic equation of the given third order linear equation is m3+5m2-3m-3=0 This is a 3rd…

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

A: The differential equation is given as follows :

Q: (6) Show that the solution of the differential equation dr 3 + dy 3(y + 1) is r (y + 1)³ + c y +1 y…

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Q: The characteristic equation of the differential equation 2 y (4) + 11 y (3) + 18 y " + 4 y' - 8 y =…

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

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: Obtain the solution to the differential equation: (3x²y² + 2y³)dx + (2x³y + 6xy²)dy = 0 x³y² + 2xy³…

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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: The characteristic equation of the differential equation 2 y (4) + 11 y (3) + 18 y " + 4 y' - 8 y =…

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Q: The Equilibrium Value for the differential equation y = (y – 4)²(y) a are O 4,0 O 4 O -4,0 O 4, -4

A: To find the equilibrium value of y ' = (y - 4)2( y ) Equilibrium Value :  Is that value where f(y0)…

Q: =C2e(-2x) - 6xel-3x) - 5e (2x) + C₂e(-2x) + 6xe(-3x) + 5e (2x)

A: option A is correct answer

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

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Q: Find the solution of the differential equation that satisfies the given initial condition. Y = (8x +…

A: To solve the given differential equation.

Q: Two linearly independent solutions of the differential equation y" + 2y' + 8y = 0 are Select one:

A: Given: y''+2y'+8y=0

Q: 5. Show that if u is any solution to the differential equation y" = -y then u² + (u')² is a…

A: See below the solution

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: Form the Differential equation if its solution is V=acos(2x +b) O a. y'= 2x b. None of these O c.…

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Q: Find the general solution of the given higher-order differential equation. y(4) – 2y" + y = 0 Oy =…

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

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Q: determine two linearly independent solutions to the given differential equation on (0,∞). Q.…

A: Consider the given differential equation, x2y′′−x(1−x)y′+(1−x)y =0 Divide both sides of the equation…

Q: %A) .{ The solution of the separable differential equation- None of the Choices y = 2² + 2 Option 1…

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

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Q: 2. (x'y* +2x²y– y²)+(x*y³ – 2x³ )y'= 0 when x = 1, y =1 %3D

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Q: 4. Solve the second order differential equation given by 2 dt2 3z = 4c", z(0) = 0, dt dr(0) 0. dt

A: We will solve the second order differential equation.

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

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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: Solve the linear Homogenous Differential Equations with Constant Coefficients: (D' -8D² +15)y = 0 a.…

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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…

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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: Determine the solution of the differential equation d5x -7 ds5 d*x d³x + 12 ds4 d²x + 8- = 0 ds² ds3…

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Q: Determine the solutions of the 1st-order linear differential equations below 3x2y′ = 2y(y −3)

A: Use separable variable method

Q: order differential equation: a. y’ = 3y + e2x           b. y’ = ___t2___           y( 1 + t3 )

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Q: Find the solution of the differential equation у" — 4у — 4х — Зех - y = Ce2x + C2e¯2x + e* + x а.…

A: Solution:

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: A population growing with harvesting will behave according to the differential equation dy 0.1y(1 –…

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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: What is the general solution of the differential equation: yiv + 6y''' - 39y'' - 124y' + 480y = 0…

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