5. Obtain the Differential Equation from the family of ellipses centered at (h,k) whose semi-major axis is twice the semi-minor axis.

Q: 2ss" + (s')² = 0

A: we will solve the differential equation.

Q: Obtain the Differential Equation from the family of lines whose slope is thrice the y- intercept.

A:

Q: dy dx 2₁ y x = x + 2√/ X X

A:

Q: 8. (x – 3y) dx + (3x – y) dy = 0; y(0) = 2

A: Homogeneous Differential Equation: A differential equation of the form f(x, y)dy = g(x, y)dx is said…

Q: 7. Let D = acting on infinitely differentiable functions, i.e., for a function f(x) * be the…

A:

Q: (x+3y - 4)dx + (2x + 6y – 3)dy = 0 O 3x + 6y + 5ln (x + 3y + 4) = C O 3x - 6y + 5ln (x 3y – 4) = C O…

A: Solve the following differential equation

Q: 5. Obtain the Differential Equation from the family of vertical parabolas whose vertex is at (h,k).

A: Formation of the differential equation

Q: 1 – 2xy)y' = yly + sinx] ; when x = 0, у %3D 1 + cosx 1+y²

A:

Q: Consider the set U = {f € Co (R)| limx→∞ f(x) = 0}. That is, U is the set of all continuous…

A:

Q: ()y -= 0 (3y²-x²* 2y4

A:

Q: 21. 36y(4) 22. y(4) 23. y'" 24. y" 37y" + 4y' + 5y = 0. 0. 8y" + 16y 2y' + 5y y' + y 25. y(4) + 5y"…

A:

Q: PLEASE ANSWER ITEM NUMBER 10 ONLY. DIFFERENTIAL EQUATIONS.

A:

Q: dx = x- y + 1 dt dy = y - x + 2 dt

A: Given: dxdt=x-y+1                       1dydt=y-x+2                       2 The above system of…

Q: y = Cje² + C2xe* + C3x²e* %D O y" + 3y" + 3y' + y = 0 y" – 3y" + 3y' + y = 0 %3D + 3y" + 3y' – y = 0…

A: Given data is: y=C1ex+C2xex+C3x2ex

Q: 3. Sole the following simultaneous ODE y₁ = y₁ + y₂ y₂ = 3y1 - y2 *

A:

Q: write the equation as two ordinary differentials for the two variables

A: An ordinary differential equation is an equation containing independent variables, dependent…

Q: 1. Use suitable substitution to solve the following differential equations: dy (b) d.x x – y - 1…

A:

Q: A tank initially contains 100 gal of brine whose salt concentration is lb/gal. Brine whose salt…

A: Given that The initial volume of brine in the tank = 100 gal The initial salt concentration of brine…

Q: III. Homogeneous DE 1. x dy + (y – 2x) dx = 0 2. (2x + 3y) dx + (3x + 2y) dy = 0 3. 3(x2 – y?) dx +…

A:

Q: aur + 2xyury + y*uyy = 0

A:

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

A: To form a differential equation from given family of curves. Differentiate given family of curves…