27. Obtain the differential equation having the solution as the equation representing all circles of radius 1 and center on the line y3x.

Q: determine the general solution to thegiven differential equation. Derive your trial solution…

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Q: Given the differential equation of the family of circles with radius of 2 units and whose center's…

A: The equation of a circle is x-a2+y-b2=r2. Here, the center is a, b and radius is r. The abscissa is…

Q: 2. Form a Differential Equation for the given equation y = 2 cosx + 5 sinx by eliminating the…

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Q: y + 3xy' – 2(y')³ = 0

A: Product rule of differentiation: (fg)'=fg'+gf' Chain rule of differentiation:…

Q: find general solution of following differential equations: y'tanx=2y-8,y(1/2pie)=0

A: Given differential equationy'tan x = 2y-8⇒ y' = 2ytan x- 8tanx         ∴ y' = dydx⇒ dydx - 2tan x. y…

Q: Find the differential equation of the cubics : cy^2= x^2 ( x - a ) with a held fixed.

A: Here c is arbitrary constant and a  is fixed. So we have to find a differential equation which does…

Q: What is the particular I solution of the differential equation (2x + y²) dx + 2xydy = 0 when x = 1…

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Q: What is the particular solution to the differential equation * + (1 + x)y = 12 with y 0 and = 0 when…

A: The solution is given as

Q: What is the solution to the differential equation 2 = 2xy satisfying the boundry condition y = e…

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Q: Suppose that y1 = e x and y2 = e −x are the solution of a homogenous linear differential…

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Q: Eliminate the arbitrary constants: y= x+ Ce2x + C2e¬x 1.

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Q: Given the differential equation of the family of circles with radius of 2 units and whose center's…

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Q: 4. Which of the following represents the differential equation of the family of parabola having…

A: Follow the procedure given below.

Q: (4) Form the differential equation by eliminating the arbitrary constants a and b from y = a sin x…

A: Eliminating arbitrary constants a & b using derivatives.

Q: What differential equation corresponds to an RC circuit with a resistor of R = 100 and a capacitor…

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Q: equation

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Q: Solve Bernoulli differential equation of y' + xy= ry². %3D

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Q: The tangent line to the curve y = x3 at the point (1,1) will intersect the x-axis at x = a.2/3 b.…

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Q: 2yy"=1+y'².

A: We have given differential equation ,  2yy'' = 1 + y'2 Here , substitute y' = u ⇒ y'' = u u'  Thus…

Q: Now find the solution of the differential equation that satisfies the conditions y(0) = 4 and y' (0)…

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Q: Find a homogeneous linear differential equation with constant coefficients whose general solution is…

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Q: Find a homogeneous linear differential equation with constant coefficients whose general solution is…

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Q: Find the differential equation given the general solution: y = cer + Czex + 3x

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Q: y > Ae* +Be* +ce; A,B and c unstant are

A: As per our guidelines we can solve only one question at a time please upload unsolved question…

Q: (3x-y+6)dx + (6x -2y-6) dy=0 hint: Case 1

A: Given differential equation is                    (3x - y + 6)dx + (6x - 2y - 6)dy = 0

Q: Find x for which the line tangent to the parabola y = 4x – x2 is horizontal.

A: In this question, we need to find the value of x at which the tangent line is horizontal.

Q: Find a differential equation whose general solution is y = cie" + cze *. = 0

A: To find a differential equation whose general solution is given by, y=c1e7t+c2e−3t

Q: 4. Form the first-order differential equation of y = e(sin y + r) %3D

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Q: Q2 Form a differential equation from the function y = (4– 2 cos x) x)cosx.

A: Given below the detailed solution

Q: y" + 25y = 5 tan²(5x) cos(5x)

A: To Determine :-  The second order differential equation : y'' + 25y = 5 tan2  5x cos  5x

Q: Solve the differential equation using only methods taught in class. y' + 3xe' = 0

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Q: 5. Obtain the differential equation of the family of circles with center at point (h,k) and radius…

A: Please refer to the image below

Q: What are the order and degree of the differential equation representing the family of parabolas y2 =…

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Q: Find a differential equation whose general solution is y = ciet + cze-4t. %3D

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Q: 2.Form the differential equation from the family of curves y² = Ae³* + Be* , where A and B are…

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Q: Form the differential equation whose solution is y = c1cosz + c2sinx Also find the particular…

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Q: Show that the differential equation dy -2 - yezy dr rezy – 2y is exact and find its solution. 3.

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Q: The solution of the differential equation 2r -y = 3 represents a family of O circles straight lines…

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Q: 2- Find the solution of these differential equations : 1. (x – y) = x + y dy dr

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Q: Show that y=x and yex are lenean inde pendent Solution of the Corres pondinp hamogeneous part ot the…

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Q: 2. Obtain the differential equation having the solution as the equation representing all circles of…

A: The solution is given as

Q: he of the curves corresponding to different values of C in the general solution of the differential…

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Q: (2x+3y-5) dx + (3x-y-2) dy=0 hint: Case 2

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Q: ,Find the two values of k for which y(x) = ekx is a solution of the differential equation %3D…

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Q: Find a differential equation whose general solution is -4t y = cjet + cze¬4.

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Q: Write the general form of Cauchy-Euler differential Equation. Solve the follow- ing differential…

A: General form of Cauchy-Euler Differential Equation. The differential equation…

Q: (4) Form the differential equation by eliminating the arbitrary constants a and b from y = aeª +…

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Q: Solve the Cauchy-Euler differential equation on the interval (0, ∞). ry" +6x²y" + 4xy' - 4y = 0

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Q: Find the solution of the differential equation that satisfiesthe given initial condition.

A: Given: The differential equation y'tanx=a+y with initial condition yπ3=a for 0<x<π2. To find:…