Find y(t) solution of the initial value problem ty' - y + 5t² cos(3t) = 0, None of the options displayed. y(t) = t cos(3t) y(t) y(t) = 5 3 5 t (1 - sin(3t)) t cos(3t) 3 | y(t) = t (1 — sin(3t)) Oy(t) = cos(3t) Oy(t) = 1 - sin(3t) y (7)=0, t>0.

Q: C₁ and C₂ are constants. For the DE y" + 12y' + 35y = sinx, (a) the complementary function is Yı(x)…

A:

Q: Show that an implicit solution of 2x sin²(y) dx - (x² + 18) cos(y) dy = 0 is given by In(x² + 18) +…

A: Given that  Equation : 2x sin2(y)dx - (x2+18) cos(y) dy = 0 and Implicit solution : ln(x2+18)…

Q: 4 (6) Find the derivative y' for the Following function 2x 1) Y = √₂²² sin (e²-1)dt 2y=1-cos (x ²-2)…

A:

Q: The solution of (e +2ay) daæ + (2 cos 2y+ 2x?y) dy is given by (A) e" + a?y² + cos 2y = c (B) e +…

A: The given equation is; (ex + 2xy2) dx + (2cos2y + 2x2y)

Q: (cos r- sin r) is a particular solution to y" – 3y' +2y = e" sin x = x2 + 3x + 3 is a particular…

A:

Q: The general solution of y" + y = e + 5e2* is y = ei (A cos (*) + B sin )) + Ce-" + 응e2x 2 () V5z y =…

A: Given that  y"'+y=e^(-x)+5e^(2x) To find the general solution

Q: Q1) Solve 1 + cos y – 2xy) dx – (xsin y + x²)dy = 0 +1

A: Given differential equation is  1x2+1+cosy-2xydx-xsiny+x2dy=0 This equation can be written as…

Q: If we use the variation of parameters for the equation y"+ y = tan(t) by solving uj cos(t) + ug…

A:

Q: The solution of (e + 2xy?) dx + (2 cos 2y + 2x y) dy is given by (A) e +x'y² + cos 2y = c (B) e"…

A: Given D.E is (ex + 2xy2) dx + (2cos 2y+2x2y) dy = 0     To find the solution of the given D.E .

Q: 2 sin(z) + V3 = o %3D

A: Given :   2sin(x) +√3 = 0               2sin(x) = -√3                  sin(x) = -√3/2…

Q: 11. (D³ — 5D² + 25D - 125)y = 504 cos 2x - 651 sin 2x

A: Given :D3-5D2+25D-125y=504cos2x-651sin2x

Q: (a) x = t* - t + 1, y = t2 Select--- v (b) x = 2 - 2t, y = VE --Select--- v (c) x = sin(2t), y =…

A: Match the graph with their parametric equations.

Q: The equation ? + sin(xy) + C = 0 is the general solution of O y' + cos (xy) = 2 (x + y) 2 (ydx +…

A:

Q: Find the general solution of y''' − y'' − y'+ y = 1 + sin x + sin 2x + ex

A:

Q: f(t) = e2t cos 5t S- 2 (s – 2)² + 25 2s + 4 s(s² + 4) %3D Ans. f(t) = (sin t –- cos t)² %3D Ans.

A:

Q: Which of the following is a solution to

A: Given,             x'=A(t)x+b(t)where          A(t)=-3-173   and    b(t)=0-3cos(t)

Q: The special solution to the equation * (D²-3D+4)y(x)= 4sin(2x) Y,(x) = Excos(2x) у, (х) cos(2x) -…

A:

Q: y=(b+x²)* +(1+x°)* ( \3x² +x – c )cos²(4x) y'=? %3D %3D

A:

Q: dy Q1/ Find dx 1. if y = u and u 4x2-2x +5. %3D 2. y = (x2 + 4)2(2x3- 1)3 %3D 3. xy + x- 2y- 1 = 0…

A:

Q: (a) (i) Use the substitution sin(u) = x + 3 to show that dx 12x + 7 -1 (x+3) V-2x² – 12x+7+c. sin -…

A: As per company guideline we are supposed to answer only one question with maximum 3 sub parts at a…

Q: 2) y"+y' - 1 = 3 cos(x)

A: 2.

Q: POS jma- 3 d 1 sin t dt %3| dx 1 1 (A) – x sin(x²) (B) sin(x²) (C) x sin(x²) (D) –sin(x²) ов O O O O

A:

Q: Can you explain how all A B C D terms are calculated

A: Solution of the given question is like as

Q: y = 2 sin(2x) +11 30 30 30 Park 8. y = cos(36) 3- 1 537x 2 424 4 sin)-1 9. y 45 . 2 34 36

A: Note: Since Multiple Questions are asked, I am solving the first question, Kindly ask other…

Q: Find the general solution dy + cos(x)y = cos(x) dx O y = 1+ ke-2 sin(x) O y² = 2 sin(x) + c y =…

A: Given differential equation is dydx+cosxy=cosx........1. We have to find the general solution of the…

Q: Use undetermined coefficients to find the particular solution to y' + 4y' + 3y = = 260 sin(2t) Y(t)…

A:

Q: Find the general solution of y" + 12ly = 0. Oy(t)=c₁e-12¹+c₂e Oy(t)=c₁e¹¹+c₂e Oy(t) = c cos 11t+c…

A: This question is about ordinary differential equation.

Q: y" + 16y2x sin 4x

A:

Q: 20. y' + 3y +2y = e' (t² + 1) sin(2t)+3e¯* cos(t) + 21. y" + 2y' + 5y = 3te cos(2t) - 2te cos(1) 22.…

A:

Q: if  x²v+sin(xu)-yv²+u³v=1 x²u-2yv=1 ، cos(xu)+yv=5  ,find dy/dx

A: