For what values of r does the function y = ex satisfy the differential equation y" + 5y' + 6y = 0? (Enter your answers as a comma-separated list.)

Q: 2. Show that y = e-6t satisfies the differential equation y" – y – 42y = 0.

A: We have to verify that y''-y'-42y=0 when y=e-6t. We know that d2ydt2=y''dydt=y'de-atdt=-ae-at So…

Q: 5. For what values of r does the function y = e™* satisfy the differential equation 2y" + y' – y =…

A: Given , differential equation       2y" + y' - y = 0   (2D2 + D - 1)y = 0 The auxiliary equation of…

Q: Obtain a linear differential equation with real, constant coefficients that is satisfied by the…

A: Given

Q: The dependent variable y is missing in the given differential equation. Proceed as in Example 1 and…

A: To solve this differential equation, substitute y'=u

Q: 1. Solve the linear differential equation of y' – 2xy = = X. swer:

A:

Q: without solving the undetermined coefficients, the correct form of a particular solution of the…

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Q: Solve for the general solution of the below differential equation. y" + 3y' + 2y = cos x

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Q: For which values of n is the function ya solution of the differential equation xy"-Kxy'-6y=0

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Q: The dependent variable y is missing in the given differential equation. Proceed as in Example 1 and…

A: Given that        y''+y'2+4=0‐‐‐‐1        we have to solve this using the substitution        u=y'

Q: For what values of r does the function y= e™* satisfy the differential equation y"- 4y'+ 2y = 0?

A: for the homogeneous differential equation, the auxiliary equation is  compare this equation with…

Q: What is the particular solution to the differential equation dx 1 + y = 2e-* with y = 1, dy -1 when…

A:

Q: Determine the values of r for which the differential equation y′+2y=0 has solutions of the form…

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Q: 3. The Bernoulli's form of the differential equation x' ydx+(3x-y'dy=0 is

A:

Q: The Bernoulli's form of the differential equation x³ydx + (3x¹ − y³ )dy = 0 is

A:

Q: Assume that the rate of change in y is proportional to y. Solve the resulting differential equation…

A: Given  dydx=ky Points on the curve 3, 3 and 4, 6

Q: Find the value of n such that when the differential equation (x+y^3)dx+6xy^2dy =0 is multiplied by…

A:

Q: Find a differential equation by eliminating the arbitrary constants A, B from the relation y= Ae²* +…

A: (a) The given relation is: y=Ae2x+Bxe2x...(1) To find a differential equation by eliminating the…

Q: Obtain the differential equation associated with the primitive y = Ae3x + Be2x + Ce*.

A: Given differential equation is we have to obtain the differential equation associated with the…

Q: What is the solution of the first order differential equation y(k + 1) = y(k) + 5.

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Q: Without solving for the undetermined coefficients, the correct form of a particular solution of the…

A: We have differential equation,   We have to guess particular solution (yp ) using undermined…

Q: Determine the values of r for which the differential equation y'-y = 0, has a solution of the y =…

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Q: What is the linear differential equation of the bernoulli’s equation dy/dx-y[1/(2x)]-y^5=0?

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Q: find the solution of the z'=xz'' - e^z'' differential equation.

A: The differential equation is z'=xz''-ez''                            ......(1) Let dzxdx=vx, which…

Q: 16. What is the particular solution of the linear differential equation y' +y = sec e", whose…

A: The solution is given as

Q: Determine the value of C for the given first order differential equation when x-2 and y=1. e#+v/ =…

A:

Q: 3. The Bernoulli's form of the differential equation x' ydx+(3x - y³ dy=0 is

A:

Q: 2. What should be A for the exact differential equation of ry + A , 2Ay – 1 dr+ y? Moreover evaluate…

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Q: 1) y=x arccos - (c is an arbitrary constant), the lowest digit that satisfies Find the differential…

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Q: Find the general solution of the first-order linear differential equation for x > 0. dy = 30x + 14…

A: Consider the given information:

Q: what is the particular solution to the differential equation dy/dx=3sin(x)(2-y)with the initial…

A: You need to apply variable separable metod to solve the given differential equation.

Q: Eliminate the arbitrary constants in the equation defined by y = ae^(3x) + bxe^(3x). Which of the…

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

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Q: 1.) Find the general solution to the first order differential equation given below. -3x 3xe 2x y' 4y

A: In the given question we have to solve the given ordinary differential equation of first order and…

Q: show that there exists a unique solution to the differential equation y'=ln(xy); y(2)=1

A: Unique solution to differential equation

Q: Let y = Cre". For which values of C is y a solution to the differential equation y" = y+4e#?

A:

Q: From the differential equation dy = x2 dx, what is the equation of y in terms of x as the curve…

A: Given: dy=x2dx

Q: The Bernoulli's form of the differential equation x³ydx +(3x² - y³)dy=0 is

A: To determine the Bernoulli's form of the differential equation x3y dx+3x4-y3 dx=0.

Q: The dependent variable y is missing in the given differential equation. Solve the equation by the…

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Q: Find the value of y for the given differential equation if the value of the arbitrary constants is…

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Q: What is the family of solution for the differential equation below? (1 point) dy 8sin4x dx a. y=-…

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Q: is there any homogeneous linear second order differential equation such that two functions e* and t²…

A: Given: The two functions and   is the solution of the second order differential equation

Q: Consider the differential equation, y'+ ty = t , with the initial condition that y(1) = 4.  Use…

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Q: What is the General and Particular solution of the Differential Equation 2x(y+1)dx-ydy=0? Where x=0…

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Q: a) Is a unique solution guaranteed for the differential equation below? Do not solve the DE. Support…

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Q: 5. The Bernoulli's form of the differential equation xdy-[y + xy ³ (1 + ln x)]dx = 0 is In

A: Given xdy-y+xy3(1+lnx)dx=0

Q: Find the special solution of ele differential equation. = 20x - 4x3 dy dx y with the initial value…

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Q: Show that given differential equation is not exact and hence find its general solution (x³ + y°)dx –…

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Q: The value of k that will make the differential equation (6xy³ + cos(y))dx + (2kx²y² - xsin(y))dy = 0…

A: Consider the differential equation: 6xy3+cosydx+2kx2y2-xsinydy=0 Comparing the given differential…

Q: 4. The Bernoulli's form of the differential equation x²dy + (2xy-y³)dx=0 is

A:

Q: 2. | Determine the general solution of the given differential equation y" -6y" = 3- cos x

A: The solution is given as