y to solve the following linear differe ] dy

Q: Given f(x, y) (8a®y + 3xyf). Compute: dx?

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Q: Use Gaussian Quadrature with 2 steps (n=2) to approximate -5 0.2 dx, xe' which of the following is…

A: According to Gaussian quadrature with 2 steps, ∫abfxdx≈c1fx1+c2fx2 Where…

Q: Evaluate e21.1.png aln(v) dx using Trapezoidal Rule with 8 equal intervals. if a = 14.49, b = 2, and…

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Q: I Solve the following FODF (x1)x*dy= (3x3y-xy +y²)dx

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Q: find all soutions of sec? (x)=VZ on the intorrel Os BK27T

A: NOTE: Refresh your page if you can't see any equations. . take square root on both sides

Q: Find a particular solution yp = Yp(x) of the following DE d'y dx? 16y = 48x + 16x + 26

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Q: Use Euler's modified formula to find an approximate value of y whenx = 0.3, given that = x+y and…

A: Given  dy/dx = x+y and y(0)=1 To determine y(0.3) using Euler's modified formula

Q: Let p and q be integers with q > 0. If y = x, differentiate the equivalent equation y = x°…

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Q: Which of the following gives the length of the curve y = Vx over the closed interval [1,4]? (A) - dx…

A: Explanation and solutions is given below....

Q: - Evaluate the follwoing | r" exp(ax")dx where a + 0 and m+l = 1, 2, 3, ...

A: Given integral is, ∫xmeaxndx Substitute, u=am+1nxm+1dudx=m+1am+1nxm+1dx=1m+1am+1nxm+1du Then,…

Q: (c) Prove that L{Cost Si(t)- Sint Ci(t)} Logs s +1 %D

A: The complete solution is in given below

Q: Solve the following DE by using appropriate substitution. Evaluate y(x) explicitly. an dy Jy – 5x +…

A: Consider the provided differential equation, dydx=y-5x+4+5 Solve the provided Differential equation.…

Q: B) Find the general solution to the following DE. dy y? + x2 = 0 dx

A: Given differential equation is y2+x2 dydx=0

Q: Solve the following problem Pu + dx2 = 0, 0 < x < L, 0 < y < H ду? ди ди (0, y) = 0, (L, y) = 0, dx…

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Q: Given f(x, y) : 5x? + 5y2, evalue the following to at least 4 decimal places. fz( – 3, 1) =

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Q: dy ,2,,2 1. х + 3y = x?y? dx

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Q: For x> 0, 음 S"규E dt = Itt? %3D

A: For x&gt;0, we need to find ddx∫1x11+t2dt. Leibniz's rule for differentiation under the integral…

Q: dz Find- at t = n, if x=21sin' 12t + 170, z=19cos12t +190t . %D dx

A: The value of sin (npi) = 0 We will put t=pi in dz/dx

Q: dy Find dz If ze" + (Inz)y + y? = 3

A: Find dydx if xex+ (ln x)y +y2 =3 We will differentiate terms and then sum them up. So, ddx(xex) =…

Q: Given that S" 4Væ dx = 152, what is fo*4Vt dt ? 3 )

A: As we know that;  the value of definite integral will not change if independent variables changes,…

Q: Show that the following DE are of the linear type and solve. 1. dx + ² = x¹ ds 2. (t+1) + s = et dt…

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Q: Use Euler method to approximate the value of y(2.2), given               ay' - by = cx2 + dx   ,…

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Q: EX Use Euler's method ( modified) to approx; mat e y' = x+y for yC1) = 1; h=o.1,13X<z withe aecuracy…

A: We Use here Euler's Modified Method to find the solution.

Q: state the arder, degree, and linearity of the filowing differe ntial squtions ) ax* 9 + asx) : 3x-4…

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Q: Ex: Salve the equation ofD-o Pelatermeth dy inzx

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Q: Suppose z is a function of x and y, and a? – y? = 2"e6y. Solve for dz dx

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Q: Show the following differontial quahion is hamegenous and Solve it: X*dy +C y-xy) dx

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Q: dz dz and ду Suppose z is a function of r and y, and tan Vy? + x2 = z"e6y. Solve for

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Q: Solve the followings P. D. dz 0 ду Z. dx? satisfying the boundary

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Q: Find the number m, such that the function y = ema is one solution of the ODE dy &y dy + 5- dx? = 0…

A: We will satisfy the solution with given ODE to get value of m.

Q: 5. Given y = af(+ 1), Find when x=1 if f(2) = 4 and f'(2) = 5. dx

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Q: Solve for the explicit solution, y = ¢(x), to the following IVP and determine its existence…

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Q: dx find . diven that x>0, using the substitution u =

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Q: - (7- dy sin2x ) dx = 0 y y

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Q: The approximation of x'e"dx by Gaussian Quadrature with n=2 is (Use c21 = C22 =1 and r21= r22

A: Given :                 I = ∫01xeexdx

Q: Solve the diferential eguation with discasfssic Of soaL (4xy-y2) dx +(2x? - 2 xy + 2y?) dy=o

A: Given the differential equation is 4xy-y2dx+2x2-2xy+2y2dy=0 This is form exact differential equation…

Q: Lind -2x+H where X- oro Zy

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Q: Solve the following DE • X – dy =2

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

Q: Given DE: dy/dx = 2x?y!/2 Determine whether there's a unique solution to IVP at point (2,4)?

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Q: Q / if w = tan x and x=4²++ Find dw dt

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Q: The identity S dyd x f, dxdy is %3D O False True

A: We need to check whether the given Identity is True or False.

Q: Q4/ Find Pe and at (3,3,3) if E = (xyz) ax + (xyz) ay + (xyz) az m²

A: Please see the answer below

Q: (a) By using the substitution, u = 1+ x*, or otherwise, find x3 dx 1+ x*

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Q: Find dy/dx in terms of x and y if ax^2-by^5=c^2. Assume that a,b, and c are all constants.

A: Given equation is-  ax^2- by^5= c^2

Q: dx dy If L = Va? + y?, = -5, and dt = 2, find dt dL when a = 3 and y = 7. dt %3D dL dt

A: Given query is the derivative of L over t at x = 3 and y = 7.

Q: Why is e^x selected as u and not e^2x (to get du /2 = e^x dx in the problem attached?

A: Consider the integral  ∫e2xe2x+3ex+2dx

Q: owing ODE is exact and solve for x(t). dx - - xtan(x) + sec(t) =0 x( dt Where a = (1+Q) with Q being…

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Q: Solve the following using Integrating Factor by Formulas. 2. y(2x – y + 1)dx + x(3x – 4y + 3)dy = 0…

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Q: Solve the following IVP: dy sin(z*)e %3D dx y(2) = V5 %3D

A: Use separation of variables method on dydx=sinx2ex3 dy=sinx2ex3dx Now integrate both sides without…

Q: Which expression gives the length of the curve y = 4x from x=1 to x = 4 ? 4 (A) [ 4x°dx (B) |V1+4x…

A: Given query is to find the expression for length of the curve.