Which of the following is a particular solution Yp to y" + 2y' + 5y = sin 5t where A; are constants determined by substituting Yp into the equation.

Q: y" z g' = Sin x COS X Solve it by using variable of parameter.

A: This is a third order non-homogeneous differential equation with constant coefficients. We will finf…

Q: 6. Solve cos.xdx +|1+= sin x dy = 0 y

A:

Q: Show that the equation is an identity.

A: x3+8x+2=x2-2x+4LHS=x3+8x+2=x3+23x+2

Q: Which of the following equations best models this situation? A bicycle tire with a radius of 40 cm…

A: The radius of the bicycle tire = 40 cm and tire rotate once every 2 seconds.

Q: is a root of the equation y2 + ycot x cos x - 1 = 0

A: Here we have to show that, y = sin x is a root of the equation y2 + ycot x cos x - 1 = 0

Q: Solve 4 sin 2x S1₁= 8 4 -1 -¹x³ + x²-x² +2 dx

A:

Q: Rewrite the following equation with the variables separated. tan(y)y' = 4 cos(x) O sin(y) dy = 4 dx…

A:

Q: 1+cos5x 4. Evaluate y'for y = and simplify the answer sin5x

A:

Q: dy -y'sinx is: dx The solution of Select one: a. y3cosx+ C O b. %3D COSX-C C. V=3 CO5X + C d.…

A:

Q: L sin cosdx 2. sin? – cos' = dx C

A: See the details solution in below

Q: If the given is y = sec2t and x = sin?t. Determine its dx²° - (Show your complete solution in a…

A:

Q: sin y = cos x (2 cos y– sin²x)

A: Given siny dydx = cosx (2cosy - sin2x)siny dydx -2 cosy cosx = - cosx sin2x…

Q: 9. Solve the equation for 0 < x S 2n: sinx + cosx = 0 10. Solve the equation for 0sxS 2n: sec?x +…

A: Given that: 9. sinx + cosx =010. sec2x+2secx=0

Q: The equation 7y" – 12 y' + y = x can be categorized as:

A:

Q: dr = b (cos(O)dr + r sin(O)dO)

A: Given dr = bcosθ dr+rsinθ dθdr(1-bcosθ) = rsinθ dθdrr = sinθ dθ1-bcosθintegrate on both sides to get…

Q: If y = sin 2x sin 3x sin 4x then find y".

A:

Q: Q7. Solve the following equations: 3.2. cos¹ 4x-sin' 4x+x

A:

Q: r Eliminate the arbitrary costants 3X 1. y = Ae cos 3x +Ce sin 3x

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.