1. A curve has an equation y = 2 x2 + 3. Find the equation of tangent and normal lines at (2,3) using Substitution of Variables and Differential Calculus

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: Find the differential equation (Family of Curves): Strophoids : y2=x2((c-x)/(c+x))

A: If a equation consists of n arbitrary constants then the differential equation of the given relation…

Q: 18. What is the integrating factor of the differential equation y' =cscx-ycotx ? a. tan x C. sinx b.…

A: This is a question related to differential equation. Based on the formula of integrating factor we…

Q: 3. Find the differential equation of a family of parabolas with axis parallel to the x-axis.

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Q: 2. Find the differential equation of the family of curves as described below. a. Family of circles…

A: As you asked multiple question I solve only the first one 2.a) We have to find out the differential…

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 family of circles having their centers on the y-axis. With an…

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Q: y = Ce * + C2e 2x + C3e * + e 2x

A: y=c1e-x+c2e-2x+c3e-x+e2xy=c1+c3e-x+c2e-2x+e2x Here, complimentary solution is  y=c1+c3e-x+c2e-2x…

Q: B. Solve for the differential equation of the following families of curves: (1) Family of parabolas…

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

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Q: Find the Differential Equation of the following family of curves 4. Straight lines with slope half…

A: The equation of straing line is given byy=mx+cwhere,m=slope=dydxand, c=y-interceptat…

Q: B. Find the differential equations of the families of curves. 5. Straight lines with slope and…

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Q: If the length of the subnormal at any point Pon the curve is directly proportional to OP² , where O…

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Q: 5. Use the variation of parameters method to find the general solution to the gi differential…

A: Topic = Differential equation

Q: 4. Find the differential equation of a family of parabolas with axis parallel to the x- axis.

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Q: Obtain the differential equation of the family of circles having their centers on the x-axis.…

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Q: Consider the following. Differential Equation Point y' = 4x2 - x (0, 3) (a) Sketch the slope field…

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Q: Find the differential equation of the family of circles with fixed radius, r=a+b,and tangent to the…

A: I am attaching image so that you understand each and every step.

Q: y dx + (x'y+')dy -0

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Q: Consider the following differential equation to be solved by variation of parameters. y" + y =…

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Q: at

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Q: 2. Find the differential equation of the family of circles having their center on the y-axis.

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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: 11. Obtain the differential equation of the family of parabolas y =x +c and sketch those members of…

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Q: find the differential equation for the following families of curves. 8. Horizontal parabolas whose…

A: Consider horizontal parabolas whose vertices lie on y-axis. The objective of the problem is to find…

Q: 5. Circles with center on the y-axis

A: Equation of circle whose centre is on 0,a isx2+y-a2=r2---(1)Differentiating (1) w.r.t  x we…

Q: Use separation of

A: Given,                     7dydθ=eysin2θysecθ.

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

A: Equation of circle

Q: The function y(x) is defined by the implicit equation x2−√ylny=1. Find its differential at the point…

A: Differentiate both sides with respect to x and solve for dy/dx

Q: Find the Differential Equation of the family of circles with center on the line y = x, and passing…

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Q: 15. x" + x = tan t; x=-(cost) In(sect + tant)

A: Given, x''+x=tant x=-costlnsec(t)+tan(t)x''=cos(t) ln(tan(t)+sec(t))+tan(t)

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: 11. Consider the curve whose equation is given below. Up to what derivative is needed to properly…

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Q: 24. What does it mean to say that dV is an exact differential?

A: What do you mean by dV is an exact differential.

Q: 1. Find the differential equation of the family of circles of radius r whose centre lies on the…

A: According to our guidelines, In case of multiple questions we are supposed to answer the first…

Q: Obtain the differential equation of the family of curves, parabolas with vertex and focus on the y…

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Q: obtained in factored form a linear differential equation with real constant coefficients that…

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

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Q: What should be A for the exact differential equation of ry + A 2Ay – x -dy y? Moreover evaluate the…

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Q: In the following problems, obtain the differential equations of the given families of curves whose…

A: Parabolas with vertex on the y-axis, with axis parallel to the x-axis, and with distance from the…

Q: Let y = f (z) be the particular solution to the differential equation = -3z'y with initial condition…

A: Consider the differentiate equation dydx=-3x2y3 Here, the objective is to find the equation of the…

Q: By using variation of parameters, what is a possible value for u, for the differential equation y' +…

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Q: 1. A curve has an equation x2 + y² – 6x + 10y +5 = 0. Find the equation of tangent and normal line…

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Q: In the following problems, obtain the differential equations of the given families of curves whose…

A: Two way parabola possible for given question Equation of parabola Y2= 4AX (y - h)2= 4a(x-0) (y-h)2=…

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.