O y= 3° + 5-3 -5 13 -2 @y=D2*- -2 1.

Q: 3. f(t) = 2e3t sin 2t – 3e3t cos 2t -

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Q: y" + 2y + 5y = t cos(5t)-6,y(0) = 1, y'(0) = -2

A: Here we use the table of Laplace transform and the partial fraction method to find solution.

Q: cos (2t + ) dt = e2t-3 4-

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Q: Solve for the general solution of (D² - 1)y = sinx using variation of parameters

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Q: y" – 2y' + 5y = 8e'sin2t, y(0) = 1, y'(0) = -1 %3D %3D

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Q: 1. 2. (D² -3D+2)y=sine-*

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Q: Solve: Tanxdy+ y°Sin²xdx=0, y(0)=1 а. у"(3-Сos2x)-2 b. у(-2х + Сos2х) -1 d. y(-1+ Cos2x) — х с. у?…

A: This question is related to differential equations, We will solve it using given information.

Q: Solve y′′ − 2y′ + y = 2sinx − cosx  , y′(0) = 0 , y(0) = 0

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Q: y" + 2y' + 5y = t cos(5t) - 6, y(0) = 1, y'(0) = -2

A: We can solve using Laplace transform

Q: tan 0 d 30. dO sec² y dy

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Q: D2 - 3D – 4)Y = sin 2x

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Q: 3x (y? + y + cos4y)dydx 3.

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Q: Q3) Solve (ysin x + y²) dx – („ - 2xy) dy = 0 + cosx %3D |

A: A differential equation of the form Mdx+Ndy=0 is said t be an exact differential equation if it…

Q: F. Solve: y" – 6y' + 15y = 2 sin 3t, y(0) = –1, y'(0) %3D -

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Q: d) y" + y = sin 2t, y(0) = 2 and y'(0) = 1

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Q: 2z2 cos 5z dz EVALUATE.

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Q: 4x + Vx Y = (a) 7x2 – 3 et (b) y = 7x³ cos x 19

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Q: Find the solution. (Dª+2D3 + 10D2)y =0. @y = c,e-+czxe¯+e"(e,cos3r +c,sin3x) y = (c,+c,)x+e*(c,cos3x…

A: To solve the given Differential equation.

Q: y′′+ 4y = 32t cos 2t, y(0) = 0, y′(0) = 2

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Q: (tan y+2)dy cos y4-9 tan² y -9tan

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Q: 2x y" + 4y' + 5y = cosx

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Q: (D³ + 3D + 4D³ + 12D²) y = 32 cos (2x) +3e3 – 16 sin (2) -

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Q: (cos2y — Зx? у?)dx + (сos2y — 2xsin2y — 2x3y)dy %3D0 - |

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Q: y" +9y = sin 2x, y(0) = 1, y(7)=-1.

A: Since here by applying the intial condition we can not get, C1 and C2 is equal to zero so this is…

Q: (b) y" – 2y' + 5y = eª cos 2x, y(0) = 2, y' (0) = –1.

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Q: (6e² + 6z+4 cos z+2)dx %3D

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Calculate x²+y² =4 and Sin (yetp) dA,D between. ty2 = 16 abore y=0 2 %3D

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Q: y"-6y'+5y = 29 Cos zt 29COS 2t 11

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Q: cos(s) d u du = ds -8

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Q: 7- y" + ²y = cos 2t, ²4; y(0) = 1, y'(0) = 0

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Q: dy 2 3 ...2 C05X +sinx...y.-(4x+5). y. ---

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Q: FIND Y(S) OF THE GIVEN EQUATION. y" + 4y = cos(t-3) +4t, y(3)=0 y' (3)=7

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Q: 3. f(t) = 2e3t sin 2t 3est cos 2t %3D -

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Q: 2. ii) (8y2 + sin y) dy

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: у"(С) — бу'(t) — 2y(€) = 4 cos 2t – 4t³; y(0) -2, y'(0) = = -

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Q: 1. (D² 2. (D² -3D+2)y=sine* -3D-4)y=16x-50cos2x :

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Q: i- y' + 2y 4 cos 2x. yT) = 3 (using Bernoulli Equation) %3D %3D

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Q: y"(t) – 6y'(t) – 2y(t) = 4 cos 2t – 4t³; y(0) = -2,y'(0) = 3

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Q: cos y dy 2. sin y+3 sin y- 18

A: Solution: The objective is to find the value of the given integral

Q: b) dr cos² #√5 + tanz c) ₁ dt (3-5t)²

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Q: y - 4y+ 4y = 2t2 + 4te2t + t sin2t

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Q: 5. y" – 2y' + y = 2sinx cosx y'(0) = 0,y(0) = 0 %3D | -

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Q: y''' + y'' = cos(2t) y(0) = 1, y'(0) = 2, y''(0) = 3

A: See the details solution in below

Q: y"+6y'+13y=150 cos(2x); y(0)=1, y'(0)=3

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Q: -3л/2 сл/2 2. I cosysin2x dy dx

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Q: sin 2ydy 5.J7-3 cos 2y 15.

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Q: y" – 6y' + 15y = 2 sin 3t, y(0) = –1, y(0) = -4 %3D

A: Given differential equation is  y''-6y'+15y=2sin3t,y(0)=-1,y'(0)=-4

Q: S-* cos(x²)dxdy = Q2): Show that 1-y2 %3D 6.

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Q: == cos(yx²) x=r* – 2t, y=1-°

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Q: 19. y" + 2y + 5y = t cos 2t, y(0) = 1, y'(0) = 0

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