a. If the Pressure produced by the gas cylinder of the motor of the rocket is governed by the below equation: P = sin* (V)cos³ (V) And the energy is given by: cV2 W = Jvi PdV i. If V2=2V1, Find W. ii. What will be W if V2=4V1.

Q: Solve the following DE by using separation of variables or method used in solving exact DE

A:

Q: Given z = (e-2) (siny), find dr -2x O-2 e 2² (cos y) O-2 e 2 (sin y) O-2 e 2 (sin y) +e-2 (cos y)…

A:

Q: Given arccot(sin(2x + y)) + arctan(cos(2x + y)) = 0, solve for dx %3D dy

A:

Q: Solve the given diffential by variations of parameters 1. y" + y = cos x

A:

Q: 1. (e)dydx

A: Now we will solve the integral using substitution form.

Q: I. Solve the heat o at with lot) - (2,t) 3TX 8TX aud Ulxio) = lo + 5 Cos - 3 Cos *

A:

Q: Find the general solution to the following Cauchy-Euler equation ty" + ty' + 9y = – tan(3 ln t).

A:

Q: L(S,(3r² – cos t)' dt)

A:

Q: Se Ce cos (sin '(x)) COs (sin

A: We need to find the antiderivative of ∫ecossin-1xdv

Q: If the RHS (Right Hand Side-the source) function of a second-order differen tial equation with a…

A: Here we have to go option wise and choose the option with; y(0) = y'(0) = 0. Clearly we can see…

Q: Use the method of undetermined coefficlents to solve the following problem. y +8y = e-8t sin t, y(0)…

A:

Q: S cos“C)dy

A: NOTE: Refresh your page if you can't see any equations. . take

Q: 1/2 Evaluate I = dx correct to 3 decimal places using Romberg's method. sin x %3D

A: Here A is the sum of the first and last value  B is the sum of other values

Q: Sect sec't dt Tari'la)

A:

Q: siny dx + (x – sin? y)dy=0

A:

Q: a. The velocity of a car in meters per seconds travelled from its origin is given by v(t) = In (t2 +…

A:

Q: Given that: z = y sin(2x) + (1+x²)e* + cos x tan¬1(y* + 1) In(y6 + 137)

A: z=ysin2x+1+x2ex+cosxtan-1y4+1lny6+137 Differentiating wrt x, we have…

Q: Solve the di fferential equation (e'+1) cosx dx+e'sinx dy=0.

A:

Q: Suppose that a y" + axy' + by = 0 has the general solution of the following form: y = x'(C1 cos (3…

A:

Q: ди If u = e* siny where x = st? and y = s²t. Find ди and at as

A: Given data: The given function is u=exsiny. The second expression is x=st2. The third expression is…

Q: 17. Determine the value of fx dy - y dx, where x(t) = (cos 31, sin 3r), 0 ≤ ≤n.

A: The given integral is: ∫X x dy - y dx, where Xt=cos 3t, sin 3t, 0≤t≤π The components of the…

Q: Solve the following initial value problems in radians by using Runge Kutta method. 3.18 dr dy…

A: Given initial value problem is3.18dydx-xdydx-2.53e-2x=sin7y6y0=6.2h=0.21780.6192≤x≤1.3446The…

Q: The position of an object attached to a spring is given by s (t) = cos(4t) — —sin(4t), - where t is…

A: The position of an object,st=14cos4t-16sin4t on the interval 0<t<3

Q: SV1- x2 sin-1x dx

A:

Q: 2 4x (a) S rdr, (b) § sin 0 d0, Cos2/3 g do, (c) St(2t – 5)" dt.

A:

Q: Suppose that the volume, V, and radius, r, of a sphere are changing with respect to time and satisfy…

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: 4 x = c,eßt + cze¬2ßt sin 2t t3

A: We eliminate arbitrary constant with the help of above differential equation.

Q: If S sin 2y cos 2y dy = =, then x is equal to: %3D

A: Hint:    sin2θ=2sinθcosθ

Q: The integrating factor of the LDE y =x-2ycotx is A cos?x B sin3x © sec?x D csc?x

A:

Q: Solve the given higher order DE y" – y" + 3Dy – 5y = e*Sin 2x

A: Auxiliary equation corresponding to given differential equation: m3-m2+3m-5=0 Roots of polynomial…

Q: dz Find a? sin(2y – 5z) =1+y cos(6zx)

A:

Q: 125. y = / V2 + cos³t dt

A:

Q: T=V3 + cos 0 is given by:

A: Trrr

Q: the Yp Vvnich OllOWing is a particu y" + 2y' + 5y = sin t where A; are constants determined by…

A:

Q: For which a, b e R is eat sin(bx) is a solution to the heat equation Uj – kuxx = 0?

A: Take the given value as U and put on the equation and compare

Q: 4. J S (esc²a – co sec 0 tand) d0 - -

A: Explained below...

Q: If P = 2 sin(10t + x − π/4)ay and Qs = ejx (ax − az)sin πy, determine the phasor form of P and the…

A: Given- If P = 2sin10t + x - π4ay and Qs = ejxax - azsinπy To find- Determine the phasor form of P…

Q: With the substitution u = sin(x), we get | 11 sin2(x) cos(x) dx = 11 u2 du. u? du. 11 %3D which…

A:

Q: implicitly, if e*(e» – 1) + sin(2x + 5y) = In(v7) – · cot(2x) 8. Find %3D y+2

A: Given,

Q: I d²u dv² tan v sec“ V

A: Find your answer below

Q: dr Solve the given differential euation: + rtan 0 = 7cos0. de %3D r = (70 + C') cot0 Or = (70 + C)…

A:

Q: Suppose that the volume, V, and radius, r, of a sphere are changing with respect to time and satisfy…

A:

Q: If L(ešt + cos(3t)) = As²+Bs+C (s–5)(s²+9) the value of C is

A:

Q: (f) If w=4x² +4y² +z² ,x= p sinø cos0, y= psinøsin0 , z =pcosø, Əw find and ap

A:

Q: Solve the di fferential equation (e+1) cosx dx+e'sinx dy=0.

A: Given differential equation is : ey+1cosx dx+ey sinx dy=0 To solve the given differential equation.

Q: If V) AT sin (2 Tf t)/(2 TfT), find the energy contained in v (t).

A:

Q: H.W. 1) Lt² sin wt 2)L t cos wt 3)L t² sin 4t 4) Lt³ cos wt .3

A: Recall the Laplace's Transformation, L{tnf(t)}=(-1)ndndsnL{f(t)} where L is LaplaceTherefore,…

Q: 20. e2= cos(z/4) dz

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.