If u = a + j13 and v = -11 – jb, calculate the value of Re (4).

Q: Find the solution of the following IVP: y(t) = dy -2ty=9t²e², y(0) = 5. dt

A:

Q: Calculate the following antiderivatives: (a) 13t – 6t - 10 dt = +C. »» / + 3.5,fa du = 1 (b) u714…

A:

Q: Find the antiderivative F(x) that satisfies the given condition. dF dx = 4e* + 4x²; F(0) = -5

A: Given query is to solve the differential equation.

Q: Find the integrating factor for the First order leaner DE- x² ay +4xy=2x³e¬*? dx e 2x2 e 4x or

A:

Q: Calculate the following antiderivatives: (8t – 5t° – 1) dt = |+C. 1 (b) + 6.5Vu) du =+0 +C. u!/4

A: Given that: (a)∫(8t-5t8-1)dt(b)∫1u1/4+6.5udu(c)∫12x5dx

Q: c.) S (4t²-t²+16t)dt/(t²+4) d.) S V1-cos*o de

A:

Q: Use the RK4 method with h = 0.1 to obtain a four-decimal approximation to the indicated value. y' =…

A: To solve the given differential equation by Runge kutta Method of order 4 first we fill find the…

Q: Use the substitution v = r+ y +3 to solve the following initial value problem dy = (x + y + 3)?, dx…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: » / 13t – 41º + 4 dt = 6. (а) 1 - 5 Jū du: (b) dx = 4x3 (c)

A:

Q: Find the general solution to da 4t +8- + 16x (for t > 0). dt? dt 1+t2

A:

Q: The general solution to d?y/dt2 = 25y is

A:

Q: Let y(x) = c1 + c2x + C3 et is a general solution for D. y" + ay' + by +cy 0, Find the value of a?

A: To answer the given question, we form a differential equation from given general solution.

Q: Find the general solution to dr tIn(t) +r = 6te". dt Enter your answer as r . ...

A: Given the differential equation             tln(t)drdt+r=6tet Find the general solution.

Q: Differentiate. R(t) = (t + et)(4 - Vt) -Vī + 2(4– Vī)(1+e') R'(t) 2t

A:

Q: Find the general solution for dø = z(z – z²)sec²Ø %3D | dz

A: the given differential equation is: dϕdz=zz-z2sec2ϕ we have to find the general solution of the…

Q: dv = 16 – v², when t 0, v = 10 dt

A: Given:

Q: Calculate . (x² + x²)e²as, where S is the cylinder with equation x² + y² = 9 for 0 < z < 10.

A:

Q: d'y dy 4+y =r²-21 +3 dt? dt

A: We will calculate CF and PI separately then we will add them.

Q: 522 – 7z+3 dz - 12 dt 15w – 13u? + w dw f) e) d)

A:

Q: If r + s2 + v3 = 12, dr/dt = 4, and ds/dt = -3, find dv/dt when r = 3 and s = 1.

A: Given: r+s2+v3=12,   drdt=4,  dsdt=-3 , r=3 and s =1

Q: (i) J. dt 6. –t²

A: We’ll answer the 1st question since we answer only one question at a time. Please submit a new…

Q: Find the general solution to t²y + (t + 1) y =t', for t > 0.

A:

Q: d²y Compute dz? at the point (1, 2) given a² – y² = -3. a) 3 b) 4 9 d) 8 e) O

A:

Q: Determine the general solution of (s +t?) ds +st dt = 0. 82+2t2 O+2s2 %3D = C O s4 +2s2t2 = C

A:

Q: Find a solution to the SDE dX; = X,(ydX; + tdt), where y ER is a constant and Xo = 1.

A: The given equation is dXt=XtγdXt+tdt. The given initial condition is X0=1. The integration formula…

Q: Calculate the LOS of y = x² + 2x + 8 LOS is x = a is b is cis

A:

Q: Find the particular solution of the DE x?dx +ydy =0, when x = 2, y 1. O 2x3 + 3y2 = 19 O 2y + 3x2 =…

A: Given, differential equation,x2dx + ydy = 0Integrating on both sides, we get∫x2dx + ∫ydy = Cx33 +…

Q: t²e*dt dz J2r

A: on solving this we get the

Q: fz? +z+1 I = dz co

A:

Q: Given z = 20t +24 and y = 90t2 + 103 da (i) dt | dy (i)- dt

A:

Q: Find the general solution of this ODE: d²y dy + 7. + 10y = 3t2 + 4t – 1 dt? dt

A: We have to solve the given differential equation.

Q: Find the general solution to Ja' (t) = x(t) – y(t) + 2e"; y'(t) = y(t) – ¤(t) + 5e';

A:

Q: V9-r² S xydzdydx •3 (d) S So

A: We have to find value of given triple integration

Q: Simplify the following expression. X d * J V4+t* dt (Hint: Vi+Pt ,2 1 +t dt = + dt + dx - X -X -X

A:

Q: ds Differentiate with respect to t and solve for dt s2 = x² + y? %3D 2s ds dt = 2x + 2y dt dt x + ds…

A:

Q: b.Introduce a new dependent variable v so that v = y/x, or y = xv(x). Express dy/dx in terms of x,…

A: Given that, v=yxy=vx

Q: Differentiate W.r.t to x ne*

A:

Q: V19+r* dt , find f'(C

A:

Q: for the -j 3 O de terminant 2-j3 3 2 i-s 1

A: det3j2-3j3-3j-120-j1-j=3jdet-12-j1-j-2-3jdet-3j201-j+3·det-3j-10-j=3j-1+3j-2-3j-3-3j+3-3=-3-6j

Q: te² i· k) dt V1 – ? 40.

A: Solving by definite integral we have

Q: dt if t = (8r' +2r² +3) and w = dw =(r* +2)*. Determine

A: Derivative

Q: Differentiate. R(t) = (t + e)(2 - VE) %3D R'(t) =

A: Given function is Differentiating both sides with respect to x by using product rule of…

Q: Differentiate e w repect to X. expression (x2+y)" (use D fur dy)

A:

Q: Differentiate R(t) = (2t + e)(3 - V). %3D Answer: R' (t) =

A:

Q: Q. Find F(s): e6t St2 cosh 4t dt.

A:

Q: Give a physical interpretation of JT. F.ndS.

A: This expression is of surface integral for calculating the area of the field bounded in the…

Q: Evaluate by using homogeneous D.E. 3 (3x? + y²) dx – 2xydy = 0 O ao3 = C(9x³ + y³) O ap3 = C(9x² +…

A: ANSWER: OPTION 2nd

Q: Evaluate ſ z dz, where C is given by x = 3t, y =t²; –1<t< 4.

A: Let us consider a complex function f(z) then the function can be written in the Cartesian coordinate…

Q: Find h t Trans form of decivative for d²f and d' f dt3

A:

Q: Q2 Given z = xw? + cos y + wx , w =t, x = 2t? , and y = 3t, find dt

A: Let's find.