Prove that the general solution of the differential equation √√1+cos(t) d0=(√1 + cos(t) — t sin(t) 0(t))dt is - -2t√√1+cos(t)+4√√1-cos(t) Se dt + C 0(t) = C 2t√√11 cos(t) 4√1 cos(t)

Q: 2x + x2 cos(x) + 1 -dx x2

A:

Q: Find the general solution of the following first-order ODE xy' = y + 2x3 sin?

A:

Q: x*y"+xy'+(x? y=x cos x 2. Show that is a solution of the equation

A:

Q: Show that (a) 8(at) =8(t), (b) 6(t) = 8(-t), %3D %3D la|

A: Consider the provided question, Hello. Since your question has multiple parts, we will solve first…

Q: y(cos 2x)e*y – 2(sin 2x)e*y + 2x + [x(cos 2x)e*y – 3] = 0 %3D dx

A:

Q: Show that there is exactly one solution f E L'([0, 1]) of the equation f(x) = 7 + sin(x) %3D

A:

Q: Verify that y(t)=C_(1)sin5t+C_(2)cos5t is a solution of y''(t)+25y(t)=0

A:

Q: Solve dN dt = (1¹ 1+ cos(2nt) N where t ≤0 and N(0) = No.

A:

Q: The complementary function of the differential equation d²y dx² 2 + 3x +y= dy dx 1 is (1-x)²

A:

Q: العنوان solve b sin ² (3x) cos² (5x) dx 2 8 tan³x dx >

A: First, we need to identify the type of integral we are dealing with. The first integral is a product…

Q: 5

A:

Q: (cos y + y cos x) dx - (x siny - sinx) dy = 0

A:

Q: π/2 g(x) = 2x + 4 sin² x g(t) dt. - n 0

A:

Q: Is the equation separable, linear, bernoulli, or homogenous? x4 + 4xy2 2x3 + x²y +y³ а. dx b.…

A: Separable equation:   A first order differential equation y’ = f (x, y) is called a separable…

Q: Solve y' = cos(2x + y – 5) – 2. = COS

A: The solution is given as

Q: Find the general solution of (2x + y cos (xy))dx + x cos (xy) dy= 0 Show your solutions on a…

A: Solution

Q: (a) a²y + y sin r = xy. (b) y = x³y - 2y³. (c) y = e²-2y (d) y'= x² + y² xy

A:

Q: Consider the initial value problem (2xy² + cos x cosy) dx + (2x2y- sinx siny) dy = 0 and y(0) = 1…

A:

Q: Solve the equation y' + a = eax +)csc(ax+y), where a is a real number Select one: a. e-(x…

A: The differential equation is given as y'+a = e(ax+y)csc(ax+y)                          (1) Let ax+y…

Q: Solve and explain how you got the solution to this initial value problem cos t dx(t) dt + sin tx(t)…

A:

Q: Solve using an integral cos²(x) + 2cos²( cos³(x) .dx

A: Evaluation of the integral

Q: f (t) =-e" sin (21 +7)

A:

Q: 1. (D² - 4D+5) (e² sin x)

A:

Q: 1. Solve the differential equation d²x dt² (a) = 10- d²x dx dx dt (b) (c) 3- dt (d dt² = ď²x dx dt²…

A:

Q: Solve the ODE with differentials operator (D²+4)y= cos(2x) + cos (4x)

A: Linear ordinary differential equation

Q: Solve 8(t – nt)cos(-) dt

A: Given integral is ∫-∞∞δt-πtcos1Tdt

Q: The general solution of x*y = -x³y- csc(xy) is A 2x?сos(xy) - 1 %3D сх B 2x²cos(xy) +1= cx² c)…

A: We have given a differential equation ,  x4y' = - x3y - csc(xy) x4dydx = -x3y - csc(xy) Here , plug…