The solution of the following separable differential equation (y − 4) 4 = (x – cosx)(y +1) is: " }ln(y2 + 1) – 4tan-Ây = -cosx+c b. ln(y² + 1) -4tan ¹y = - sinx + c c. In (y² + 1) - 4sin-¹y = d. None of the - sinx + c

Q: The complementary function(C.F.) of the differential equation(D – 8)°y = sin 8x is (ci + c2x +…

A: Solution: The objective is to find the complementary function of the given differential equation

Q: y = (C₁ + C₂x) eª + sinx+x²; y" - 2y' + y = −2 cos x + x² − 4x + 2

A: Here we find the first and second derivatives of given solution and then put in the left hand side…

Q: A ball is drawn randomly from a jar that contains 5 red balls, 7 white balls, and 4 yellow balls.…

A: From the given information, there are 5 red balls, 7 red balls and 4 yellow balls. The total number…

Q: For each of the following differential equation find all equilibrium solution and determine whether…

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Q: 5). Write the first-order differential equation in standard form. (Use yp for y'.) −xy' = (8x + 7)y…

A: To find- Write the first-order differential equation in standard form. -xy' = 8x + 7y + xex…

Q: general solution of the differential equation (6xy^3+2y^4)dx+ (9x^2y^2+8xy^3)dy-0. Use the…

A: Solve by homogeneous method

Q: Identify which below is a separable Ordinary Differential Equation 2xy a. y': х(у — 1) — у dy _x+ y…

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Q: 83. Solve the differential equation x+y=(-x² cos x)y². = x(sin²x+C) A. y 1 C. --=x² y

A: Given

Q: Solve the differential equation (d2y/dx2) - 7dy/dt = 0 if y(0) = 1, and dy(0)/dt = 1 A.…

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Q: Determine the form of a particular solution to the differential equations. Do not solve. (a) x" – x'…

A: (a) The associated homogeneous differential equation is                     x''-x'-2x=0…

Q: Consider the differential equation (1– v2)y' – ytanx = yv²tanx Which of the following is the linear…

A: Given(1-2) y1 - y tan x = y2 tan x —(I)(1-2) y2- y1 - y1-2 tan x = tan x —(II)Put       y1-2 = u…

Q: Solve these differential equations d. dy/(√x ln⁡2x )+dx/(y^2 ln⁡y )=0 e. xdx+ (ydx-xdy) cos⁡ (y/x)…

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Q: If 2x3+3ycos(xy)+(cx2y2+3xcos(xy))y'=0 is the exact differential equation then c =?

A: The exact differential equation is defined as the differential equation of the form Mx,ydx+Nx,ydy=0,…

Q: Solve the ordinary differential equation 3xy" + (2 - x)y' - 2y = 0. Then evaluate the first four…

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Q: The standard form of the differential equation cosx y' + cosx y = x sin x is: None of the above O…

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Q: Solve the ordinary differential equation 2xy” + (1 - 2x2 )y' - 4xy = 0 . Then evaluate the first…

A: To solve this ordinary differential equation we use substitution method. Then we find y(x)  Then we…

Q: Find the solution r(t) of the differential equation with the given initial condition: r'(t) = (sin…

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Q: Find the general solution of the following differential equation: a) t * dy/dt = (1-y^(2))^(1/2).…

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Q: A solution of the Ordinary Differential Equation x?y'' - 2xy' + (x² + 2) y = 0, x > 0 is defined by…

A: 4th option is correct. y_p= xcos(x)

Q: Find a particular solution of the following differential equation using variation of parameters meth…

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Q: The standard form of the following linear differential equation sin x = (cos x)y + xsin x + 2 is: dx

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Q: Determine whether the following ordinary differential equation (15x - tan(4x))y"' - x²y" + 7y'…

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Q: 1. Evaluate 3 √² 13 0 |3x² - 12 dr.

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Q: Solve the ordinary differential equation  3xy” + (2 - x)y’ - 2y = 0 . Then evaluate the first three…

A: Given differential equation is 3xy''+(2-x)y'-2y=0                         (1) ⇒y''+2-x3xy'-23xy=0…