dy By Picard's method, the third approximate solution of = f (x,y). y(x,)= y. is dx .a None of these .b V; = %o + ] f (x,y, )dx, .C V3 = Y2 + | f (x. y,) dx, .d V3 = Yo + | f (x, y2 kdx,

Q: find Df, R1 3 1y = (x4)² + 5 2) y = 5-2x 3) y = - X- 2

A:

Q: Minimize Q = 8x² +4y2, where x + y = 12. O A. x=0; y= 12 O B. x= 4; y =8 O C. x= 12; y = 0 O D. x=…

A: Given, Q=8x2+4y2  , where x+y=12

Q: ind positive constants b and n, such that 3n + 2 n.

A: Finding the values of b and no

Q: 23. Let f(x) = 3x - 1 and g(x) = x – 2. (a) If f(2x) =g(3x), find the value of x. (b) If H(x) =…

A: Given:fx=3x-1gx=x-2 To find: (a)   If f2x=g3x, find the value of x (b)   If Hx=3fx+2gx and Ha=5,…

Q: y uf f(x,y) = -+2 then find y %3D ду? O a. 02f 2x %3D dy? .3 O b. 22f %3D dy? y3 O c. a2f dy? y? 2x…

A:

Q: 4. Find the general solution of (x³ + y³) dx = 3xy? dy A. -3x3 + 2y3 Cx B. 7x3 + 2y3 = Cx C. -6x3 -…

A: According to question, Given differential equation, x3 + y3 dx = 3xy2 dy

Q: 2. If w = f(x + ct) + g(x- ct) show that c²wxx = Wtt C= constant.

A:

Q: 8) 2x+5y=5 x-4y=9

A:

Q: 1. (2л + 5у)dA %3D? D YA (0, 4) у 3 (x + 2)2 X = y - 16 D (-2, 0) (0,-4)

A:

Q: Could you help me solve and understand d-f?

A: d.The required value is calculated as follows:

Q: Let y(x) = c1 + c2x + C3 et is a general solution for D. y" + ay' + by +cy 0, Find the value of a?

A: To answer the given question, we form a differential equation from given general solution.

Q: -3x+9y+6z = 18 -2.x – 3y + 2z = -8 4.r + 6y-4z = 68

A: To solve for x, y, z.

Q: iv) if zy = (x) then z, + Zy = 5 mark

A:

Q: iv) if zy = (x)-1 then zx + Zy = %3D a. x – y b.x + y c. -z2(x + y) d. z²(x – y)

A:

Q: %3D =D3e %3D 4.

A:

Q: Suppose x andy are variables satisfy the equation x2 - y = 12. What is 3x3 dy A %3D dx 2y dy 3x4 dx…

A:

Q: 5 Given yz - Y1 = m(x2 – x1). Soive for x2- %3D

A: Given y2-y1=m(x2-x1)

Q: 2. Determine C when x-y%3D0 show the solutions. (xy + x)dx = (x²y2 + x² + y2 + 1)dy

A:

Q: 7re9 + 7y lnx, then is given by:

A:

Q: 2 5. x = 1+t2 2 y= t(1+t?)

A:

Q: Determine the particular solution. (xy)dx + (x² + y2)dy= 0: x = -1, y = 2 O 8 = 2y2(x2 + y?) O8= y…

A:

Q: he equilibrium pul 12) P(x) = -2x + 8, S(x) = 3x + 2 %3D

A:

Q: Given f (z, y) = 3z + 2y +1, find the value. f (3, 2) The value of f (3, 2) %3D

A: We have to solve

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.