What is the differential equation of the family of parabolas having their vertices at the origin and their foci on the x-axis. A. 2x dy – y dx - o B. x dy • y dx = 0 C. 2y dx – x dy - o D. dy/dx – x = 0 Select one: а. D b. A С. С d. B

Q: d*y dy a) da4 + 4y = 3.x2 dx dy dy b) + 4y = 3x4 dx dx? dy c) dæ? + 4y = 4x3 dx d*y d) dr4 dy + 4y =…

A: The solution is given as

Q: What is the differential equation of the family of parabolas with their vertices and foci on the y –…

A: To find the differential equation of family of parabola with their vertices and foci on y axis.

Q: Which of the following is NOT a separable differential equation? A (xy+y) dr= (x2y² + x² + y²+ 1) dy…

A:

Q: c. x²y″ − 3xy' +4y=0, _y(1)=5, y′(1)=3. - - d. x²y" — 5xy' + 8y =8x6, y(½)=0, y′(½¹⁄) = 0.

A: (c) A differential equation is given by, x2y''-3xy'+4y = 0 with initial conditions y1 = 5 and y'1 =…

Q: A-Find the solutions of the following differential equation for the given initial conditions, ý = -y…

A: The given differential equation is dydx=-y(y-6) with y(0)=8

Q: Form the differential equation for the function y = a sin3x -bcos3x O a. y" - 9y 0 O b. 9y" + y = 0…

A: Given differential equation is: y=asin3x-bcos3x                                                (1)…

Q: (a) Draw a slope field for the differential equation dy = 2x - y, using the grid below. dx %3D (b)…

A:

Q: Which of the following most nearly gives the differential equation for all parabolas with vertex on…

A: Given

Q: Which of the following is NOT a separable differential equation? dy =xy2 dx А dy - =x- 2y dr B ye2*…

A: Answer is option B) dy/dx=x-2y

Q: Find the order differential equation of ddy] 6 dy dy dy +7. + 6- 3. +7 = 0 dx3 dx2 dx

A: Given that a differential equation and find the order of this differential equation. We know that…

Q: Suppose that x 0 is a regular singular point of the differential equation x²y"-x(x+3)y' + (x+ 3)y =…

A:

Q: Which of the following differential equations has two real and equal roots? Felect one: O a. d'y 4y…

A: Here roots of differental equations means roots of auxilary equation  A quadratic equation…

Q: Consider this problem: r²y" + xy/ + ? = - 0, y(1) = 0 y(2) = 0. a) Place the differential equation…

A: The differential equation given here is x2y''+xy'+λx=0 y''+y'x+λx3=0 compare it with equation…

Q: (a) Use the fact that 5x? - y? = c is a one-parameter family of solutions of the differential…

A:

Q: Obtain the differential equation of a parabola with axis parallel to the x-axis. A 3(y")²-y'y"=0 B…

A:

Q: What is the differential equation of the family of parabolas having their vertices at the origin and…

A: If y=f(x), then the independent variable x is called the input of the function, and the dependent…

Q: The differential equation for the family of curves y = Cx – 4 is 2y + 8 %3D ху Find the family of…

A:

Q: The integrating factor that transforms the differential equation 3y" – 6y' + Axy = 0 , into a…

A: The differential equation of the form, A(x)d2ydx2+B(x)dydx+C(x)y=0 can be transformed into a…

Q: A-Find the solutions of the following differential equation for the given initial conditions, ý = -y…

A: Given y=-yy-6dydx=y6-y⇒dyy6-y=dx⇒161y+16-ydy=dxIntegrating we…

Q: Solve the following first order differential equations, clearly showing all calculation steps dy…

A: Given that differential equations and we find the solution of this differential equations by using…

Q: Which of the following is a third degree partial differential equation? aw A Əx3 ду dz B) dr?, Əz…

A: The degree of the differential equation is represented by the power of the highest order derivative…

Q: Which of the following is a linear differential equation? O da-t{1+t²) sec² ædt = 0 O…

A:

Q: Which is the differential equation of the family of parabolas with axis along the y-axis and with a…

A:

Q: (a) Find the general solution of the differential equation (dy)/(dx) - (2y)/(x - 2) = (x - 2)3. (b)…

A: (a) Given- dydx-2yx-2=x-23 To find- The general solution of the above differential equations.…

Q: Which one of the following differential equations is NOT linear? .A dy xy² = In(x) dx - .B dy…

A: Option (A) is correct.

Q: Determine the differential equation for the family of parabolas along the y-axis. O (zy' – y)* = 16…

A:

Q: Obtain the differential equation of the given family of curve: y² : C-x a. 2x³y' – 3x?y – y³ = 0 b.…

A: Given curve : y2=x3c-x ⇒c-x=x3y2

Q: What is the differential equation of the family of lines whose sum of the intercepts is fixed as k ?…

A: Given:  What is the differential equation of the family of lines whose sum of the intercepts is…

Q: Verify that the indicated family of functions is a solution of the given differential equation.…

A: Given d2ydx2-6dydx+9y=0    ;  y=c1 e3x+c2xe3x

Q: Which of the following is/are exact differential equations? a) xexydx+yexydy=0 b) (x+4x3siny)dx +…

A: Since you have asked a question with multiple parts in a single request we would be answering only…

Q: Which of the following is NOT a separable differential equation? A(x-2y) dr+ (2r +y)dy=0 B xy dr –…

A:

Q: Which of the following is NOT a separable differential equation? A x3y dy=e' dr (e2"+4) dy=y dx ©…

A:

Q: Obtain the differential equation of the families of parabolas with vertex and focus on the y-axis. O…

A: Explanation of the answer is as follows

Q: Consider the following first order differential equation dy dr -- 4y = 2ry What is the asymptotic…

A: The given differential equation is, dydx - 4y =2xy2         ............1 Divide equation (1) by y2…

Q: Which of the following is NOT a separable differential equation? (A) (x- 2y) dx + (2x+ y) dy=0 B) xy…

A: We know that an equation which is dependent and independent variables get sepreted is a separable…

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

A:

Q: Which of the following equations can be reduced to the homogenuous linear differential equation with…

A: Differential equations are given, we have to find homogeneous linear differential equation with…

Q: Which of the following is the homogeneous differential equation? A. (3x - 5)dx = (4y - 1)dy B. xydx-…

A:

Q: Which of the following most nearly gives the differential equation for all parabolas with vertex on…

A:

Q: The differential equation for y = Ae3 + Be9r is: %3D o y'+12y'+27y=0 o y'-12y'+27y=0 o y"-12y'-27y=0…

A: Differentiate given equation twice w r to x

Q: Solve the dy *+g+ 3 differential %3D equation.

A: The given problem is to solve the given differential equation. Given differential equation dy/dx…

Q: . x dy/dx - (1 + x)y =xy²

A:

Q: For which of the following differential equations isoclines are the equation of lines passing…

A: In the equation of the form y'=f(x, y), the isoclines are lines in (x, y) plane obtained by setting…

Q: Which of the following is NOT a separable differential equation? A x²y dy=e" dr (e2"+4) dy=y dr ©…

A: From the given differential equation,we have to the equation that is not separable.

Q: Which of the following is a homogeneous linear differential equation? D³(D2 – 4)y = 3x+ 2e¯3x | о у"…

A:

Q: Obtain the differential equation of the family of circle with center on the x-axis ? a. yy"…

A:

Q: How are the constants a, b, and c related if the following differential form is exact? (ay2 + 2czx)…

A: To Determine: how are the constants a,b and c related if the following differential form is exact?…

Q: Which of the following equations is NOT a variable separable differential equation? A B (x² − yx²)…

A:

Q: Q3 /Write Only the (Order and Degree) of the following differential equations a) (d'y/dx')23 -…

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.