(h) Yk+1 – Yk = kek,

Q: F(s) = (8s + 11)/[(s-4)(s²+9)] %3D

A:

Q: y' + 2y = e*,

A: Note: Since you asked multiple questions, I solved first one if you want answer of other questions…

Q: Find high order DE 6. (D4-5D² - 36)y = 0

A:

Q: y" + 2y' +y = e-*

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

Q: 2. -1z"cosdz zl=1

A:

Q: 6. S -3dy 2y2+14y+70

A:

Q: тахz %3D 2x + у S.t х+у<60 2х + у 2 40 y < 30 х, у 2 0

A: Linear programing is a mathematical techniques to optimize solution of given constraints.

Q: (tVE2 + y² – y)dt + (y/E² + y² – t)dy = 0o %3D |

A: We will find out the required solution.

Q: d²y - y = у 3 10sin?x %3| dx2

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

A:

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

A:

Q: r/64–x² r61-x²-y² x dz dy dx -67+x²+y²

A:

Q: V1-y² -1 0 kpxpzp (,x + zA),I „«-,S

A: The given integral is: I=∫-11∫01-y2∫0x y2+x2 dz dx dy

Q: L[(t + 1)2e] = ? %3D s2-1 s2 +1 (s-1)2 (s – 1)2 -

A:

Q: | d²y +y³ = 0 dx² is not linear. صواب İhi

A: True

Q: 2 Find dyif y.+3x-7 and x =, 2t +1

A: As per our guidelines we are supposed to answer only one question.Since you have asked multiple…

Q: y(t) = y" - 3y' = 8e²t - 2e-t, y(0) = 1, y'(0) = -1

A: Given

Q: b, y" -zy'-3y= e*

A:

Q: 4' for T- T2• T, and T- T1• T2. x - 5y, 4x + 2y) y, 0)

A:

Q: 6z ry- (y² zi + j+k) -i do 6.

A: The surface is defined as, x2+y2=42z=1z=7 The plot is a circular quadrant as observed in the…

Q: +2x (D³ – 4D’D'+ 5DD" - 2D") z=e** + Vy +x.

A: Given PDE is D3-4D2D'+5DD'2-2D'3z=ey+2x+y+x We can write it as D-D'2D-2D'z=ey+2x+y+x             (1)…

Q: 4. Find dyax and d2 x =V4- t , go t²-2t ye t'-2 get'.

A:

Q: 3 V9-y s S f(1,y)dxdy. y)dzdy. y-3

A:

Q: 23- y" - 2y + y = 0; y₁(t) = et, y₂(t) = tet

A: 23. Given y''-2y'+y=0   Also given y1t= et,  y2t=t et   To verify: the functions y1, y2 are…

Q: px + qy=z-a √x² + y² + z²

A:

Q: O': Find the general yy' – 2y² = e²

A: A first order Bernoulli ordinary differential equation is of the form dydx+pxy=qxyn Where p(x) and…

Q: 5. (D2 – 5D + 6)y = 18x2 + 12e2* (Assume yp = Ax² + Bx + C + Ee2x)

A:

Q: Qs) y" + 3y' + 2y = e* – 3

A: See the details solution in below

Q: y³dy 2. S. (a²-y²)7

A:

Q: + d²z Oy2 = 0;

A:

Q: F(x,y) = -41² - 2xy-4y² +z+y.

A: Follow the procedure given below.

Q: Evaluate (D2+3D+2)y=(1+e-x)-1

A:

Q: dx What is the best substitution to evaluate V2x 2х - х* |

A: Given I=∫dx2x-x2If we consider x=1+sinθ and dx=cosθdθthen,I=∫dx2x-x2=∫cosdθ2(1+sinθ)-(1+sinθ)2

Q: 6) qyo -x² +2x + S%y +62=0 sty

A: 6)

Q: (у-3) dy y2-6y+1

A: To evaluate the integral: ∫(y-3)y2-6y+1dy Solution: ∫(y-3)y2-6y+1dy…

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: Q16 3 a) / 3²+ 2dt dt c) /,₁ (3-5)²

A:

Q: Vy² – 25 dy y3

A: SINCE YOU HAVE ASKED MULTIPLE QUESTIONS IN SINGLE REQUEST, WE WILL BE ANSWERING ONLY THE FIRST…

Q: (D - 2D + 4)y = 0 ; y= - 2, Dy = 8, D²y = 0, when x = 0.

A:

Q: 2x³y' = y(y² + 3x²) using Bernoulli.

A:

Q: %3D18 SK+y%= {x-zy=9 11

A: Given query is to find the solution of the system.

Q: 41 82x-x2 9V x²+y? dydx =

A:

Q: dy 6. S: y3-2y2

A:

Q: Find DF of fcx,y)=x²e° at the point (-2,0)-

A:

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: 523 + 222 – 5 y = dy then dz 3x + 2

A: Consider the provided equation, y=5x3+2x2-53x2+2 Find the derivative of the equation with respect to…

Q: Find formulas for dy and Ay if y = x² – 7x + 3.

A: To give the formula dy = f'(x) dx and    ∆y = f(x+∆x) -f(x)

Q: y = (2x + 1)v2x+1

A:

Q: Q = - ST 8-x²-y² x² + y² y dz dx dy

A:

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.