a. Obtain the differential equation of the family of straight line with the algebraic sum of the intercept fixed as k.

Q: show that each function y = ƒ(x) is a solution of theaccompanying differential equation. y' = y2 y =…

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Q: Prove that the differential equation is not exact ey (e" + ") - s/ = 0 2+ + -

A: Exact diffretaial equation

Q: Straight lines with slope half the value of the x-intercept

A: The equation of a line is defined as y=mx+b, where, m is the slope and b is the y-intercept.

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 general solution of the differential equation of (z + y?) dr + rydy = 0 (22

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Q: Find the differential equations for each family of curves under the following conditions: c)…

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Q: 2. (D? — 2D + 5) у — 252? + 12

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Q: (D² – 3D + 2) y = (1+e-*)?

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Q: Suppose that f(t) is a solution of the differential equationy′ = ty - 5 and the graph of f(t) passes…

A: Given, y'=ty-5 And f(t) is a solution of the differential equation. The graph of f(t) passes through…

Q: 2. Solve the first-order linear differential equatio a. y' + 3y = e3x

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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: c. y" +4y=tan2x %3D

A: Solution of the given differntial equation is

Q: Construct a linear first-order differential equation for which all solutions are asymptotic to the…

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Q: Find the differential equation that has y = C1 + C2x as its general solution.

A: To find the original differential equation we  have to eleminate the arbitrary constants by…

Q: The differential equation of the family of curves orthogonal to x² + y? = C² is

A: Solve the above questions.

Q: Find the differential equation of the following families of curves: y2(b+x)=x2(3b-x)

A: Given y2(b+x) = x2(3b-x)                 (1) Differentiate equation (1) with respect to x , we get…

Q: at

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Q: 3. Plot the slope field for the differential equation = y² – x and sketch the solution for the…

A: Given: A differential equation dydx=y2-x. To sketch: Slope field of given differential equation and…

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

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Q: a. y = C,e=x + Cze-2x + x

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Q: Which of the following is  x^2y''+4xy'+2y=2lnx Euler's differential equation converted to a 1st…

A: Which of the following is  x^2y''+4xy'+2y=2lnx Euler's differential equation converted to a 1st…

Q: Solve the Euler-Cauchy differential equation d²y dy 3x- +4y = In2x- Inx %3D dx

A: Given: Let us assume, x2d2ydx2-3xdydx+4y=ln2(x)-ln(x)......(1)

Q: State where in the ty-plane the hypothesis of the (non-linear) Existence and Uniqeness Theorem is…

A: Given: The given differential equation is y'=t-y2t+5y

Q: Verify that the function y = Ce5x is a solution of the differential equation           y′ = 5y

A: The given function is  y = Ce5x  The differential equation is y′ = 5y

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: Find the solution to the differential equation   that passes through the origin.   z=

A: As the solution function to the given differential equation, passes through the origin we will have:…

Q: Obtain the implicit form of the differential equation of the following relation: y -3=x³(3e* +c)

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

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

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Q: 4. Find the differential equation of a family of circles, each having its center on the line y = x…

A: To find the differential equation of a family of circles, each having its center on the line y=x,…

Q: 1.3x – xy = c -

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Q: Find a differential equation whose general solution is y = cje% + cze¯74. = 0

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Q: Consider the differential equation 2²y" – x(x + 2)y + (x + 2)y = 0, x > 0 - 3.

A: Given: x2y''-xx+2y'+x+2y=0, x>0   To find: A second solution y2x using the solution y1x To show:…

Q: e. xy' – y = x*y"

A:

Q: Find the differential equation for the family of: 1. Cav.. HAIS 2. 3. Curves cy? = x²(x - a) in…

A: Differentiate given curve with respect to x.  And eliminate a.

Q: 2uvdv + 2u?du – v²du = 0 %3D

A: Given that: 2uvdv+2u3du-v2du=0

Q: Show that: a) The price of the stock itself, that is when u(t, X1) = X1, solves the…

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Q: The Complementary Function of the differential equation - 8 + 15y = e is %3D

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Q: Let y' – 35y = 7x*e5x. Is this differential equation pure-time, autonomous, or nonautonomous?

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Q: Obtain the differential equation whose general solution is y = C1 + C2 e^.

A: The given general solution is                y= c1+c2e3x We want to find the corresponding…

Q: The roots of an auxiliary equation are m1=4, m2=m3=-5. What is the corresponding differential…

A: If the root of the auxiliary equation is m1=α and m2=β, then the corresponding differential equation…

Q: Find the terminal value, lim y (r), for the solution of differential equation dy + 3z'y - 6z". dr

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Q: Determine the interval for which the solution of the differential equation  y(iv) + 4y''' + 3y = t-1…

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Q: 4. x" +x=e+!.

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Q: Determine whether the statement "The differential equation y′ = xy − 2y + x − 2 is separable" is…

A: Determine whether the statement "The differential equation y′ = xy − 2y + x − 2 is separable" is…

Q: Verify that y = (x³ – x) In cx satisfies the differential equation (x³ – x)y' – (3x² – 1)y = x5 –…

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Q: Obtain the differential equation associated with the given function: y = Cx² + C².

A: first we will derivative with restive x then find the value of C then put in given equation

Q: Find the particular solution that satisfles the differential equation and the initial condition.…

A: The given differential equation is  f'(x) = 8x f(0) = 9

Q: (D² – 2D + 5) y = 25x² + 12

A: Given: D2-2D+5y=25x2+12 So,  The auxiliary equation is: m2-2m+5=0 Now solve; m2-2m+5=0m1,…