du d2u Solve the following ODE problems (Here, u' u" , etc.): := dt du (а) + 2u = 2e-t, u(0) = 1. dt (b) и" + 6и"+ 5u' %3D 0, и(0) — — 1, u" (0) — 0, u" (0) — 2. -1, u'(0) = 0, u" (0) = 2. (с) и" — 2и %3D еt - cos(t). COS

Q: (c) 2ry'y-y²+²=0.

A: 2xy'y-y2+x2=0⇒2xyy'=y2-x2

Q: 1. Solve the following DE's (for y as a function of x, where possible): a) xy'= y – 2y, with y(1) =…

A:

Q: 2 The derivative of y = 3x? 3 + 3x is 2x 3 A. y =** 2 2 3 x° + x´ +3 3 4 4 В. у B. y' = +3 2x2 + 3x…

A: Derivative.

Q: Find y as a function of x if x'y" + 5xy' + 4y = 0, y(1) = 9, y'(1) = -2. y =

A: Solution :-

Q: (a) y 10u² and u = 5 - ² (b) y = √u and u=1-1

A:

Q: (a) -3r*, (b) x* + 4r3 + 6x2 + 4x + 1, (c) Ar10 + bx+c (A, B and C are constants).

A:

Q: Provide an appropriate response. Find the derivative of y= Oy = 9x2 + 8x-3 Oy=9x2 + 8x-3 9x² y' =…

A:

Q: Find general solution to Cauchy-Euler equation: (t^2)y''-2ty'-3y=t^2

A:

Q: can you explain if this is true or false if y=x2+y2, then y'= 2x+2y

A:

Q: 1. Use the basic differential properties shown in section 3-5 to find each indicated derivative. (A)…

A: According to our guidelines, we can answer only three subparts of a question. Other parts can be…

Q: If New Hampshire's population was 1.4 million in 2018 and there were 1.3 million motor vehicle…

A:

Q: Find y as a function of a if y" - 3y" y + 3y = 0, y(0) = -7, y' (0) = -4, y" (0) = 9. y(x) =

A:

Q: If xy? + yx2 - 2= 0, then dy/ dx =.... Jika xy2 + yx2 - 2= 0, maka dy/ dx =.... 1. О…

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.