Use Eulenis methed to caleulate the first thnee value problem Size. Caleulate ke 1. approximation to for the speei fhes incre nent ex act solution. y +2x), Y(1) inttial en dx = 0 - 1 2 Y=? Y2-2 All have teo write 4 decimal places ? Y(exact)=? बोि

Q: 5. y-2y+y-6e* d'y dy 6. 2. dx2 +2y e2x d'y dy 7. 2 -2y D4e 3x *

A: 5. givend2y(x)dx2-2dy(x)dx+y(x)=6exThe general solution will be the sum of the complementary…

Q: 4.) Solve by separation of variables: x' = x cost where x(0) = 1.

A:

Q: 0.7.8: Solve: dA HP а) = -10A, A(0) = 5 b) 3 ЗН, Н(0) 3 1 dt dx d²y с) = 4y, y(0) = 0, y'(0) = 1 dx2…

A: “Since you have posted a question with multiple sub-parts, we will solve the first three subparts…

Q: S(4 sec x + 3 tan x)²dx

A: We will solve the problem

Q: 10. A trough with length of 15 m is filled with water. The ends of the trough have a parabolic shape…

A:

Q: + xy' + y = 8 Inx

A: Consider the given differential equation as x2y''+xy'+y=8lnx. Since the differential equation is…

Q: dy x*y3 = X dx and y(0) = 2.

A: find the solution of the given differential equation

Q: 7. 3s+4 L-1{ s²+4s+5- 2t a. e²t (3 cost - 2 sin t) b.e-2t (3 sint 2 cost) – c. e2t (3 sint 2 cost)…

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Q: 2) Fad the Center i Radius of the Crck delined by x*sy'sX+v== DO NOT need to draw the Circle.

A: Try to make the given equation as standard form of equation of circle and than compare with it.

Q: 3. Show that sinh a + sinh y = 2 sinh cosh %3D

A:

Q: (1 + ху) dx — (1 + х?) dy %3D 0.

A: (1+xy)dx-(1+x2)dy=0(1+xy)dx=(1+x2)dydydx=(1+xy)(1+x2)put y=vxdifferentiate w.r.t.…

Q: 14. The f'(4) for y = v3x2 + 1

A:

Q: D. Evaluate et-2 tan vE 2t + 3 S 't² – 2t + 1 e2t

A: To evaluate: ∫et-2e2t, tan tt, 2t+3t2-2t+1dt=∫et-2e2tdt, ∫tan tt dt, ∫ 2t+3t2-2t+1 dt+A,B,C

Q: 9. The surface area of a cylinder is A = 2h+2². If the radius is measured to be 6 inches with a max…

A: Given, Surface area of cylinder, A=2πrh+2πr2 Given radius r=6in with maximum possible error dr =…

Q: LH.S.-R.H.S. HW/ Brove-that: (1) 1-tanhf x sech'x 12 11

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Q: 21 dy d²x = 2(3+x² 2 dy xy)/x³

A: See the attachment

Q: 5) [xe*dx (Use Integration by Parts) 6) If [g(x)dx = (8x“ + 2)* +C, find g(x).

A: We will use integral by parts to solve the first given question and differentiation to solve the…

Q: solve Bernaulli's Единстоп ху=хчу 3 dx dy - - 3

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Q: dz Find if yz – In z = x + y ax

A: To find the partial derivative of z of yz-ln z=x+y with respect x, differentiate yz-ln z=x+y, while…

Q: The families of curves represented by the solution of the equation dy dx for n = - 1 and n = + 1,…

A: To determine the families of curves represented by the solution of the below differential equation…

Q: Find the solution of: 1. 2xyy' = 1+ y² when x = 2, y = 3

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

Q: / 45T7COSキ-JT7Sint -4Jiは Sint+Cst ー1 17 17 4517cost-ST7sint 1457 sint aJ(7 cost 17 17

A:

Q: l, arctan( y/x) dA, where R = {(x, y) |1<x° + y° < 4, 0 < y< x} %3D

A:

Q: contour integration

A: We have to solve the given integral by contour integration. Given integral is ∫0∞cos2πxx4+4dx