S(x+1)² + (y – 4)² = 16 L(x + 1)? – 12 (y – 2)? = 0 1.

Q: F(s) = (8s + 11)/[(s-4)(s²+9)] %3D

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Q: Find the particular solution for y' = x3 – 2xy when x = 0, y = 1

A: We are given a differential equation: dydx=x3-2xywith the initial cobdition x=0, y=1 We can solve…

Q: Higher Order L.D.E (D2-2D+10)2y=0

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Q: 3 L cosh-t|= 4 .a 4s 4s2 – 9 - .b 4s 4s2 – 16 .C 9s 9s2 – 16 .d 16s 16s2 – 9

A: We have to solve given problem:

Q: 3x2 +- 8(y + 1) = 0 dy y+1 C 3(: 100 - designed by freepik 24C X=Yi+(x20)

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Q: dy 2ty ii) 12+1 - 21 – (2 – In(t² +1)) = 0; y(5) = 0

A: Differential equation of the form Mdx+Ndy=0 is said to be exact if ∂M∂y=∂N∂x Given differential…

Q: y = 8e*, on x e [0, 2]

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Q: So So = 12x?y3 dx dy Select one: O a. 4 O b. 1 C. 3

A: Here we have to evaluate;  I=∫01∫0112x2y3dxdy=?

Q: (2) y" (t) - cy'(t) + gy(t) = 6t²²t where: you) = Y(u) =

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Q: d²y 54. Let y = 4r+2r+l_find CL)

A: To find the double derivative of below expression.

Q: S Sz(x² + y³)dxdy, wherein B = {(x, y) E R²; 0 < x² + y² <4}.

A: Double integral

Q: b) y =1+ f(z)=2x-2 O 1ks f-(z)=-1 O 2 34s (2)=2x-1

A: Step 1 Replace y with x and x with y  Step 2 Then solve for y in this equation  Step 3 Replace y…

Q: dy * + 2(t + 1)y² = 0, _y(0) = - ip 1/8

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Q: Calculate y*)(0) for 0 < k < 5, where y = x* + ax³ + bx² + cx +d (with a, b, c, d the constants).

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Q: What is ∫3x(x2+2)5 dx? Do not include the constant "+C" in your answer. For example, if you found…

A: Given integral ,    ∫3x x2+25 dx        Let , x2+2=z=3∫ x2+25.dx            ⇒2x dx=dz=3∫z5.dz2…

Q: of Chal) D x24 6x -2:0 ent

A: Solve x2+5x-2=0

Q: Q.4 (a) Evaluate (+4+16r²+20x+9 dx. (x+2)(x +3)?

A: Let us solve the integral ∫3x4+4x3+16x2+20x+9(x+2)(x2+3)2 using partial fractions.  The denominator…

Q: d*y 4. Find dx 1 if y=x' + 5 +13 2x? 3x 5

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Q: 2. x y-3xy = 4x + y+1 at (0, - 1)

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Q: y" + ay' t sy = g e-2^ + 8 %3D ylo) ay'6o) =

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Q: = -21e 2 C D +4 D +9D t1o)y 4. /f x-O -4 l 10

A: To sove the initial value problem for y=y(x)

Q: 10. (D² – 2D – 3)y = 0 when x = 0, y = 0, y' = -4

A: To find the solution of the given differential equation .

Q: flx)= X + 2 Lix-1l if 0Lx<3 %3D 0LメL3 what is C (o) ?

A: Given query is to find the value of f(0).

Q: Q1) L-1 s(s a) cosht -1 b) 1-cosht c) (cosh2t - 1) d) (1 - cosh2t)

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Q: Q1: 2ty 2t – (2 – In(t + 1)) y = 0 y (5) = 0 t2 +1

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Q: V16-y? /32–x²–y² V 22 dz dx dy

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Q: e + xy + 4x = 1 ise y"(0) =?

A: ey+xy+4x=1 Differentiating with respect to x, we get…

Q: 4". Sy' 8y Sx'e* y10)=8, y'l0).S X-

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Q: √y² +9 dy 4 X using reciprocal substitution

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Q: 3. D'y - D'y- Dy + y = 0 (AD4

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Q: NOTE: Enter the exact answer. 7 V49–x² r65-a²–y² x dz dy dx 0, –33+x²+y²

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Q: • ["* [*, [° 42²y — 2²³ dz dy dz J1 1. Evaluate

A: NOTE: As per our guidelines, I have solved the first problem. If you want the answers of rest,…

Q: Qs) y" + 3y' + 2y = e* – 3

A: See the details solution in below

Q: a.) = y° (4 – y²) - b.) y' = y In(y+ 2) %3D c.) = (ye" – 9y)/e" -

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Q: v x +y = 2xy + 4x; at x = 1 and y = 3

A: Since you have asked multiple question As per our policy, we will solve the first question for you.…

Q: d'y 11. +2y = 4cos² x dx

A: Given:        d2ydx2+3dydx+2y=4cos2x

Q: L(cosh 4t) = %3D s²+16 .b O s²-16 .C s2 – 4 I. .d O s2 - 8 SI

A: We will find Laplace transform of Cos hyperbolic function

Q: 4. y = vx + 2 x,for-

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Q: d'y (3x* – 5)(2.x² +9x–6) Determine the of y = 3 dx 7x

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Q: . lim 4y9 + V y--00 /y18 – 1

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Q: 11. (D² + D – 2)y = 2x – 40cos (2x) 12. (D? + D)y = -cosx

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Q: 3 1 (x + 2y)dydx -1 a) 5 b)7 O d)-:

A: Please check step 2 for solution.

Q: 2.2 nd, from first principles, fa(3, –1) for f(x, y) = 4x²y² + e®. |

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Q: So Ve Pollowing the D.E 3X 3y' = e - \2 X +39

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Q: Y1 (x) = 8a + 2x; y2(x) = x In(bx); y3(x) = ca?.

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Q: Calculate y(k)(0) for 0 ≤ k ≤ 5, where y = x4 + ax3 + bx2 + cx + d (with a, b, c, d the constants).

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Q: (D² – 4)y = 2 – 8x; when x = 0, y = 0, y' = 5. %3D ANS. y = e2x – e-2* + 2x – }.

A: We have to find solution of given differential equation.

Q: 1. If g (2) = 59 and fg'(x) dx = 25, what is g(5)?

A: Since you have posted a multiple question, we will solve the first question for you. If you want any…

Q: (b) Evaluate |(2x+3)V x² + 3x – 5 dx , by using substitution method.

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Q: 1. (D² + 4)y = 4cos' x

A: