Q2: * Q2: y" + ay' + by = f(t) Find a,b and f(t) so that Ypı = et +t? – 1, Yp2 = e2t + t? – 1 %3!

Q: 50 (e*-2)(e2x + 1) et dx

A:

Q: Let h(x) -222+z+4 %3D ,what is h' (-5)? 2+4z-1

A:

Q: y®y' – 8y9 = ex ,8,

A: On simplification, we get

Q: Find

A:

Q: S Sifoo-gool dx O d2 (f.g) = Sup {/fox) - gox|} V£₁9 € [0₂4] if d, (fig) = Find Ⓒd₁ (√x,x) @d₂…

A:

Q: get

A:

Q: 2 L₁ (2x - e²x)² dx A. B. C. D. 31e¹+36e²+3 12e4 31e¹+36e²-3 12e4 31e4-36e²+3 12e4 31e¹-36e²-3 12e4

A:

Q: pk Ph (x)=k! T(m-k+1) (k+m+1) m X \x X

A:

Q: Q2/Determine: 1. L-1 s²+9s+2 2. L-1 L(s+3)(s-1)2. s+1 (s-1)s²]

A: 1. To find the inverse Laplace transform of a given function, we would generally break down the…

Q: 1 If f(x,y,z)= of then x-y-3-

A:

Q: 6) L (x- 3)(x + 2)? dx

A:

Q: 3-J (х* + 2х 3) dх

A:

Q: Differentiate y = In(x³ + e*) .2 3x+eX А. x3+e-X 3x2-ex В. x3 +e-X 3x2-e-x C. x3-e-X 3x2-e-x D.…

A:

Q: Yob) a) fog)(x) & 3. = (x)) JI 2. x+2 (x)6 8 %3D then find

A:

Q: 2/3 = z/15

A:

Q: If X~BET(1,2) then E(X)= (1 2/B (1/B

A:

Q: Given f(z) 3D 1-홀 (7+ 3x) + 을(7+ 3x)2- (7+3x)" then f'(z) =. -을 + 꼴 (7+ 3z) -(7+3x)2+ | .... -글 +…

A:

Q: Sn( Lin el0x=ydydx = In(5) fIn(3)

A: Given integral is ∫0ln5∫0ln3e10x−ydydx. We have to evaluate the double integral…

Q: x/2 – x) · (e*² + x) dx = et + C 3

A:

Q: S(x-ae )Vx² + 2e" dx -ах - ах 11.

A: Let's find.

Q: If the dependent variable goes up when the independent variable is increased this is a(n)

A: If the dependent variable goes up when the independent variable is increase, this is an estimating…

Q: then A(-2u - 20) = -2 ---B 5 and Au 3 Au = 2 4

A:

Q: Find the sum H=p+q+rand calculate average value of the function f(x),

A: In this question we have find the average value of function f(x) in the given interval. here we used…

Q: (x*. In x dx = ?

A: Solution

Q: 9" -४ - 24 = x %3D

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

Q: (2.00-x) Vq₂ = ±xV|q₁|

A:

Q: L₁ (2x - e²x)² dx

A: Given integral is ∫-10 2x-e2x 2 dx

Q: 5x 3x2 (3x²)' ework Diffeventiate the equntion. /3

A:

Q: In this section, we showed that the rule d/dx1xn2 = nxn - 1is valid for what values of n?

A: given that ddxxn=nxn-1

Q: Suppose that Var(X) = 704.85, Var(Y) = 9161.83, and Cov(X,Y) = 2154.62. What is Var(.97X + .03Y)?

A:

Q: (*") = (") + G) + 5. Prove + 2n2. %3D

A:

Q: S (2 +ల1) 2) dx

A: We have to find the value of indefinite integral

Q: Suppose that Var(X) = 869.03, Var(X) = 7850.84, and Cov(X,Y) = 2238.69. What is Var(.67X + .33Y)?

A: GivenVar(X)=869.03Var(Y)=7850.84Cov(X,Y)=2238.69

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.