61. Show that the differential equations y' = 3y/x and y' = -x/3y define orthogonal families of curves; that is, the graphs of solutions to the first equation intersect the graphs of the solutions to the second equation in right angles (Figure 10). Find these curves explicitly. FIGURE 10 Two orthogonal families of curves.

Q: Show that ¢(x) = Ce³* + 1 is a solution to dy/dx – 3y = -3 for any choice of the constant C. Thus,…

A: We have to check Q(x)=Ce3x+1 is solution of given differential equation.

Q: first-order

A: Given : y' = x9y + sin(x) The standard form of first order differential equation is  y' + p(x)*y =…

Q: Select the differential equation that matches the given slope field. Is 1 141 O=-(2+1)*y? o -- 0--点

A:

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Q: Suppose !=sinh2r, z= 6ư, 3s= cos2r are solutions of a linear homogeneous differential equation with…

A:

Q: Write down a differential equation of the form dt all other solutions diverge from y = 4 as t →∞.…

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Q: 5. Which statement is true about solutions of y(x), as a differential equation whose slope field is…

A: Correct option is A

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

A:

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

A:

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

A:

Q: x²(a+x) 2. Family of strophoids with the equation y² %3D a-x

A:

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.…

A:

Q: Suppose that x = 0 is a regular singular point of the differential equation 4xy" + 2y' + y = 0 Then,…

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

A: Solve the above questions.

Q: 1. Draw and obtain the differential equation of a circles having its center on the line x =y and…

A: 1.

Q: (D² + 4)y = Sinx

A:

Q: Show that the differential equation UTM dy -2 - ye rey - 2y dr is exact and find its solution.

A: Use the concept of exact differential equations.

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

A:

Q: A nomal is drawn at a point P(x, y) of a curve, it meets the x-axis at Q. If PQ is of constant…

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Q: Obtain the differential equation of the family of straight line with the algebraic sum of the…

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Q: obtain in alinear differential eqaution with real, constant coefficients that is satisfied by the…

A: The solution of the problem is given in the next step.

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: 3. ydx+(1+x)arctanx dy= 0

A:

Q: 4. y" + 4y = sin² 2x when y () = 0; y' ( = %3D

A:

Q: Find the equivalent differential equation for all tangent lines of the parabola y = x^2

A:

Q: Suppose that a hare starts at the origin (0, 0) and runs with speed Vh along the y-axis toward a…

A: This question is from differential equation.

Q: If m1, m2 are the real and equal roots of the auxilary equation of second order linear differential…

A: Let us consider the second order differential equation y''+py'+qy=0 To solve the differential…

Q: Obtain the differential equation of all straight lines with alebraic sum of the intercepts fixed as…

A:

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: What are the roots of the characteristic polynomial for the differential equation y" + 4y' – 5y = 0?

A: Given differential equation:-   y" + 4y' -5y = 0

Q: Suppose sinh 2x, y2 = 6x, y3 = cos 2x are solutions of a linear homogeneous differential equation…

A: To find the differential equation :-

Q: x³y" + 3x?y" = 2x +1

A:

Q: (f). Verify if the differential equation given by 10x°y* + e¬Y + 3 sin(4x + 3y))y' + (6x²y° + 4…

A:

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

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Verify that the indicated function y = (x) is an explicit solution of the given first-order…

A:

Q: Find the differential equation whose complete solution is y=c1e-x+c2ex+4x using elimination of…

A:

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

A:

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: Obtain the Differential Equation of all circles passing through the origin and (0,8).

A:

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

A:

Q: 4. Obtain the Differential Equation from the family of curves of the form y = xC

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Q: find the differential equation of a family of parabolas with an axis parallel to the x-axis

A: We have to choose the correct answer from the given option according to the given condition

Q: y"-4y = 0; cosh 2.x, sinh 2x

A:

Q: Obtain the Differential Equation from the given general solution. y = C¡ cos(4x) + Cz sin(4x) + Cx…

A: Use the following formula, to find the solution. ddxcosax=-asinaxddxsinax=acosaxddxuv=udvdx+vdudx