Re z dz, C the parabola y = 1 +3(x – 1)² from 1+ i to 3 + 3i

Q: 2) y^2 = 4x, x^2 = 4y; revolving around the x-axis. Use washer method.

A:

Q: Check for homogeneity and obtain the general solution. (Let 4C=C) (x² + y?)dx + xy dy = 0

A: The given equation is; (x2+y2)dx + xy dy =0

Q: nd and classify the eguilibriam solutions to: dy -y° - ly dx 2

A:

Q: Find the regions of the (x, y)-plane where the equation ey. + e*. dxðy + 2e2". +x³. + e*-Yu = 0 ду |…

A: The given PDE is        ey∂2u∂x2+ex∂2u∂x∂y+2e2x∂2u∂y2+x3∂u∂x-(x+y)2∂u∂y+ex-yu=0. A second order PDE…

Q: Exercise: Use reduction order to find a second solution y2(x) 1. y" + 16y = 0, yı = COs 4x

A:

Q: 1. Find the area bounded by the parabola y?=4ax, the x-axis, and the lines x=4a, x=9a. 2. Find the…

A:

Q: H-w lo Find the dliscontinaitg point of &Cz) : ニ それそ+ 5(2+i) 2+ci-2)Z -2i の %3D

A: discontinuity of complex valued function

Q: Consider a closed rectangular box with a square ba a. Find an equation for the surface area of the…

A:

Q: + PC)U= @X) U" 00 slove this equation by central euler method

A:

Q: Q: Use Lagrange's Formula to Prove that : 1) Y = Y3 – 0.3 * [ Y5 – Y_3] + 0.2 * [Y_3 – Y_5] . -

A:

Q: his équilibriüm b. For what (positive) value of v is v solution is called the terminal velocity.) c.…

A: The differential equation satisfying the velocity of the object is given by, m⋅v't=mg+fv Here…

Q: What is the annihilator for y=x e*cos 2x ? (D²+5)2 ® D² +5 © (D²-2D+5)2 D D2-2D+5

A: See the solution.

Q: Calculate , e6x*+9y dx dy, where D is the interior of the ellipse () + ()< <1. (Use symbolic…

A: According to the given information, it is required to calculate the given integral.

Q: O Use the bisection method to numerically solve the nonlinear equation .1.5 f (x) = 40x3 –875x+35000…

A: Rffthh

Q: Bonus Home merk 2 Solve the following a Riccatí equation: including dy ーy+xy + dx ylo) =1 %3D where…

A:

Q: Solve this equation: ди + a = at %3D u(0,t) = 0 %3D ди (L, t) = 0 az u(z,0) = 2 %3D

A:

Q: Exercise: Use reduction order to find a second solution y2(x) 1. y" + 16y = 0, y1 = cos 4x

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

Q: 9. x=t² +1, y = 3t² + 2t . d y b) Find dx? Show All Work and Give Answer In Simplest Form.

A:

Q: 3. Check for homogeneity and obtain the general solution. (Let 4C=C) (x² + y?)dx + xy dy = 0

A: We will solve the problem

Q: ii) Find the area of the surface obtained by rotating the curve y = e-, -1<r<1 about a) the x axis…

A: Curve:                           y=e-x2,-1≤x≤1

Q: cos 2z dz, C the semicircle |z| = 7, x2 0 from - πί to πί

A:

Q: Find the solution y(x) of the I.V.P y"-y = 1, y (0) = 0 and y (0) = a %3D 3Da

A: First we find complementary function then particular integral and then general solution.

Q: Solve x'y" - 3xy' +4y = 0; y(1) = 5; y'(1)= 3 Using y=x" Aux Equation yc= C, XM, + CaX"a m2 or yc L>…

A:

Q: integral. 2y (2 + 6x2 + 8y²) dx dy Jy

A: Given: ∫02∫y2y2+6x2+8y2dxdy

Q: SOve the exact DE and Give the general Solution. ay-3x)y'-3y=D0

A:

Q: coordinates with dV= r dz d 4-(x2 + y2). Draw the solid

A: Using the volume of cylinder and the solid is given as,

Q: of Find and dy f(x.y) = /2x + 3y? df (Type an exact answer, using radicals as needed.) dx II

A: We can solve this as follows:

Q: ransformation, the solution y(t) of the followim y'-3y = 1, with y(0) = 2 %3D %3D (s) such that

A:

Q: Determine the state of degree then solve all the homogeneous equation: y а. у' x+vxy b. xydy = (x² +…

A: The given differential equations are  a.          y'=yx+xy b.           xydy=(x2+2y2)dx The order of…

Q: dy sin(r-y). dr Q(3) Find the general solution of %3D

A: we have to solve the given differential equation

Q: y" (E) + 2y, Ct) -4y, Ct)= 0 C)+y, (t) -3y, CE) = 2 Solve using the resoluh'on by eliminah'on

A: For the solution follow the next steps.

Q: 1. Test IlI. Solve the sys: fx-y%3D2 y = 1. x+y=7 1o the foll

A: As per our guidelines we are supposed to answer only one question.Kindly repost other question as…

Q: Homingquatlam from and bo onother coordinates. X= 4y9 243y=D9 3=4x V= tano > V=S V 6 CSCO

A:

Q: Q3- By using the Lagrange method , find the general solution of P.D.E (x – y)p+ (x + y)q = 2xz . %3D

A: According to question,Given equation,x-yp+x+yq = 2xz

Q: 4- fil0,00)→R all continious Aunction aro Sx³f(x?)dx= Sx f(x) dx %3D show this.

A:

Q: What is the annihilator for y=x e*cos 2x ? A (D2-2D+5)2 B (D2+5)2 © D2-2D+5 (D D2 +5

A: A detailed solution is given below.

Q: Given the IVP 1+2xy + (y + x²)y' = 0 : a. Show that the DE is exact. fy = Ix = %3D b. Find the…

A:

Q: Find the solution of: y+y=2e'.y(0) = 0, y (0) =0 Select one: a. y3sint-2cost + e' O b. %3D C. y=…

A: to find the solution of the given differential equation

Q: } Identify (write down) the type of DE, and find the general solution. (у - 3x)dy %3D (x + Зy)dx

A: Type of DE is, homogeneous &amp; linear and order is 1.   The solution is provided below :

Q: Re z dz, C the shortest path from 1 + i to 3 + 3i

A:

Q: 2) y^2 = 4x, x^2 = 4y; revolving about the x-axis. Use washer method.

A: To find the volume of the solid generated by rotating the region bounded by: about the x-axis.

Q: 4. Given: x³y'" – 3x?y" + 6xy' – 12y = 2x* + Inx , what are the roots of the equation. A. m = 3,2 ±…

A: 4) option  D.

Q: dx x2 + x+ 1 (a) analytically, (b) single application of the trapezoidal rule, (c) composite…

A: I am solving the first 3 parts.please resubmit the question for other parts.

Q: A) Solve The Following Equation By (Lagrange Method): пр + ди = 2(x + y)u и %3D и (х, у) и дх ду и…

A: We’ll answer the first question since the exact one wasn’tspecified. Please submit a new question…

Q: Elimin ate th e parameter from the param etric equations x = E, y = 4t +2;0 sts4.

A:

Q: What is the annihilator for y=x e*cos 2x ? A D2+5 B D2-2D+5 © (D²-2D+5)2 (D² +5)2

A:

Q: What is the annihilator for y=x e*cos 2x? A (D2+5)2 B D2+5 D2-2D+5 D (D²-2D+5)2

A: Explanation of the answer is as follows

Q: a) f(z) = 14/(z + 2z + 2) is a complex function, find (1/T) S-000 14/(x2 + 2x + 2)dx

A: Solution a: Given 1π∫-∞∞14x2+2x+2dx We have f(z)=14z2+2z+2 Considering ∫Cf(z)dz=∫C14z2+2z+2dz then…

Q: How do you find a cubic function for the quation ?(?)=ax^3+cx^2+d that has a local maximum value of…

A:

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.