y? x² 4 Find dV , where E is the solid y2 x2 + 4 z2 - <1. 9 + +

Q: 2-x2 Evaluate Jenyz dy dx x²+y? 2 Select one: a. Non of them b. 1 /2 C.

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Q: Using substitution show y = 1+ Ce-t² is a solution to dy + 2ty = 2t dt

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

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Q: (3) Solue the Initial Value Probles -that SatieSFies the Compleme equation (+) yM -2(x+ Dy! 13 ! %3D…

A: We are given a nonlinear non-homogeneous second order ordinary differential equation, which we have…

Q: 2x3 + 11a? + x +9 x + 2 Given x2 +1 (2a3+ 11a2 + x+ 9 dx Evaluate (Don't forget to include the %3D…

A: use substitution method for solving the integral

Q: H.W1:- y':= x+2y by using Euler method find y(2.5)? Where h=0.1, y(2)=3

A: I am only solving the first question.please submit the question again for the other parts.

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: 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: (xq + X2 Y1 +Y2° 2' 2 The formula for a segement on the coordinate plane is M =

A: The midpoint formula for a line segment joining the two points (x1,y1) and (x2,y2) is given by…

Q: [+]。 + y² = 0 Ans:Order3 degree2, ordinary, non-linear d³y (4) +4 dx3

A: Given differential equation is d3ydx3 + 4dydx3 + y2 = 0

Q: y ( 2 ) d X To obtain the general solution of [xsin() ycos(-)]ás + » dx + xcos X What will be the…

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Q: r/6 c1 .3 y sin z dx dy dz 0. -2

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Q: h 2, k -1 and r 5 %3D (x - h)2 + (y- k)2 = r2 %3D %3D wwww x2 + y2 +Dx +Ey + F 0

A: Given:- h=2, k=-1 and r = 5 To find:- Equations of circle in form (x-h)2+(y-k)2 = r2  x2 +y2…

Q: (x^2+y^2-3)dx-2xydy=0 Prove the given DE is exact, and find general solution

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Q: 15x2 — х3 — 43х — 19 Ах + В C The integral (x + 1)²(x² – 6x + 13) dx can be rewritten as lax² + bx +…

A: Given integral, ∫15x2-x3-43x-19x+12x2-6x+13dx

Q: '4 I x1/2 dxi n = 8 (a) Approximate its value by using the Trapezoidal Rule.

A: Given: ∫04x dx where n=8 To find: The approximation using the following, a) Trapezoidal rule, b)…

Q: dy We wish to find the solution to dæ = x°y that passes through the point (x, y) = (1,3).

A: We need to evaluate integral.

Q: 3. Obtain the general solution 3 3 y.(x .y + 2-x – y) dx+ 3 - 2).dy = 0 x (xy |

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Q: dx (z+2)v²+4x Evaluate z+2| O 2 sec-1 + C |z+2| O None of the choices. Please refer to my solution.…

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Q: xp dt of dy A particular solution X, where XeC1 -2t dt Select the correct answer.

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Q: 8. (/E= + y² - y) dt + (y/E² – y? - t) dy = 0; when t = 3, y = 4 %3D

A: Solution is  ty=3(t2+y2)3/2 -363

Q: 4 d°y _134% + 6y = 0 dx %3D dx3

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Q: Q/homogeneous D.E equation X dy y2

A: we have to solve the given differential equation.

Q: 2 4) d?y |1+ () dx2 dx, Find the: Туре: Order: Linearity: Why?: Unknown Function: Independent…

A: Topic:- differential equations

Q: 2. [f 5y ey dA, F- {(x, y): 0 s x s y?, 0 s ys 2} F

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Q: t sect df 2/ V3

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Q: Find the solution. d3x d?x dx – 2–=0 dt + dt3 di2 -21 ® y = c,+c,e'+c,e- -31 D y = c,++ce+c,e-2

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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: Non-Exact H.W: (2xy ey+2xy³+y)dx + (x²yey-x³y²-3x)dy=0

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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>…

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Q: 8y2 + 3 dy /6 – 2y

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Q: ii- Using Solution by Variation of Parameters find y" + y = sec x = using: ccs x Yp(x) = -y, 2" W…

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Q: Solue (x+1)y" + xy -y =0 ; yco)2, 4'c0)= i ginen that either e* or e-x is a solution of (x+D y" +…

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Q: Determine the solution y(t) of the IVP then find y'(t). 2y'' + 3y' − 2y = e4t cosh3t,        y(0) =…

A: Ordinary differential equation involves derivative with respect to one variable.

Q: 2y4+x4 etermine the classification of the given DE, y' = and solve in the хуз n of M(x,y)dx +…

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Q: Q5. Calculate L-1 -2s e s2 Q6. Find general solution of the DE 4.x?y" + 8xy + y = 0

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Q: 5. Solve y' = x² + y, find y(0.1) by talking step size h = 0.1 given that y = 10 at x = 0 %3D…

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Q: b. Homogeneous Coefficients y(x2 + y?)dx + x(3x2 - 5y2) dy = 0; when x = 2, y = 1

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Q: y_2/n (y + 2) +x-lux = C Solve the equation using separation of variables D x dy (1+x) y dx x/1_y)…

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Q: * y"-2xy'+uy = 2, yto)=0, yl)=1 =)ytx)=? %3D find the solution using numerical solution

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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: 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: (D³+3D²– 4D)y = 0 -4x Question 5 Find the solution. dy 31+9y=2ty 5/3 dt

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Q: V4 – a2 - x2 valuate f, S Sva-a - ° ( + 2²) kz dz dy dæ – a2 – 3y? (y + z2) kz dz dy dx

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Q: y' cos(4x) + y, y(0) = 7 The Taylor solution is: y = ao + a1x + aɔx² + a3x³ + o(x*) where: ao =| 7…

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Q: z = x+ y dy _ x+ y+2 1. Using substitution solve the equation which satisfies the condition y(1) =1.…

A: Use the given substitution to convert the homogeneous differential equation into separable form then…

Q: ey-x y' = 1+ e2y ,y(0) = 3 %3D (h=0.01) .What is the error in the solution?

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Q: z = x+ y dy_ x + y +2 1. Using substitution change the dx x+ y+7 to a separable equation, Hence…

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Q: 04/ Determine the particular solution of the equation d²y dx2 = 9 given the boundary 3 dx conditions…

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Q: Q.3 Find general solution by separating the variables. i. y3 = (y* + 1) cos x dx. ii. y' = 3x²(y² +…

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