6 1. Express the equation in cartesian coordinate r = 3 cos 0 + 2 sin 0 2. Express the equation in cartesian coordinate r = sec @ tan 0 3. Express the equation in polar coordinate x²(x² + y²) = y² dy 4. Solve the differential equation dx - sec x = 0 5. Solve the differential equation 6. Solve the differential equation 2xy dx + x2 dy = 0 (1+r) dy 7. Solve the differential equation dx y 4y" - 25y = 0 8. Solve the differential equation 9y"-30y+25y = 0

Q: Determine the phase shift of the function y = sin(x - π/3)

A:

Q: y" – 9y = t° – t e + sin(3t)

A:

Q: Solve sin(x) +7 sin(x) cos(2x) = 0 for x E (0, 5). Give your answer in radians correct to 3 decimal…

A: The given equation is sin(x)+7sin(x) cos(2x)=0 and the range for x is (0, π/2).

Q: Find the form for a particular solution to the equation y "+2y'– 3y =r?cos (nt). A…

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: 1.) Solve the equation on the interval (0, 2x): cos" 0-sin' 0+ sin-0. 2.) Write the equation of the…

A: Note:-As per the Bartleby expert guidelines for Answer the question is only one and if subparts is…

Q: Eliminate 0 from the equations : (i) x = h + a cos 0, y = k + b sin 0 (ii) x = a ser³ 0, y = b cot³…

A: Solution is given: Hope the solution is helpful.

Q: 2. (sin 0-2r cos 0)dr + r cos 0(2r sin 0 + 1)d0 = 0

A:

Q: Solve y" – 4y' + 8y = e2" + sin 2x 3.

A:

Q: 3x² sin(2y) + (2x³ cos (2) + - (22:²³ + ²) y' = 0.

A:

Q: cos²x sinx dy + (y cos³x - 1)dx = 0

A:

Q: Solve the following equations y" - 4y + 4y = 8x² + 4x y" - 2y - 3y = sin 2x

A:

Q: Calculate ㅠ 2 6³ cos² (4x) sin² (4x) dx

A:

Q: Solve: y" + 2y' + 2y = 2 sin(x) +3 cos(2x)

A:

Q: Equation y" - 2y + 2y = exsinx (5) (21 2 2 Appropriate Form of the Particular Solution

A: We need to solve Differential equation. As per Bartleby guidelines we can solve one question from…

Q: Use differentials to approximate the value of cos 29°.

A:

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

A:

Q: Q1:-/ Verify by direct substitution that y, = epx cos qx and y2 = ePx sin qx , are solutions of the…

A:

Q: cos²x sinx dy + (y cos³x − 2)dx = 0

A: Given problem:- cos2(x) sin(x) dy+(ycos3(x) -2) dx=0

Q: dy' dx (6.) (i + cos x ) = X = 0 y = 1 sinx (sinx tsinxcosx -y) Answer: C=1/12/2

A:

Q: ry"+xy'+(x* -y =0 -)y = y = x cosx is a solution of the equation Show that

A: Given               x2y''+xy'+(x2-14)y=0                      (1)

Q: (cos y+ y.cosx-ec*.sin x)dx+(sin x – xsin y)dy =0 cos.x

A:

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: Find the phase shift of y = -2 sin (4x -) 2, 2n units to the left B) units to the left C) - units to…

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: (1 point) Check by differentiation that y = 3 cos 2t + 3 sin 2t is a solution to y" + 4y = 0 by…

A:

Q: Question 2 Find the solution to the DE. (y-x+xycotx) dx + xdy=0 xysinx=C+ sinx - xcosx Oy=(c +…

A: Concept: For a differential equation of the form P(x,y)dx+Q(x,y)dy=0 The differential equation is…

Q: Find y' and y". . sin3y=x²+tany+1

A:

Q: A suspension bridge swinging in the thunderstorm can be modelled by the following equation:…

A:

Q: y = eVx+cosx

A: To  findderivative of1)y=ex2+cosx

Q: Find the solution. (D³ +7D2 + 19D + 13)y =0; when x =0, y=0. y' =2, y"=-12 A y = e-2'sin3x B y =…

A:

Q: Graph the epitrochoid with equations x  =11 =cos t - 4 cos(11t/2), y = 11 sin t - 4 sin(11t /2)

A:

Q: (r+sin 0- cos 0) dr + r (sin 0 + cos 0) d0 = 0

A: (r+sinθ-cosθ)dr+r(sinθ+cosθ)dθ=0 lets rearrange and then integrate