1- Find the solution to the vibrating- string problem With Uu = c*uxx , u(0, t) = u(l, t) = 0 3nx u(x, 0) = sin- 1. ,u(x, 0) = sin 0

Q: dx 1)y /sec(3x) 2) y = Vu + 2u , x= u? - 3u

A: Definition used -            Chain rule of derivative -                             ddx(f(g(x))=…

Q: Ou :? u =x +y +:, x=e" cos 21, y =e"21, : =e" = e" (cos 21-sin 4t +&t +8) +2e Ob. e (cos 21 - 2 sin…

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Q: a2f дхду' a2f 2. (a) If f (x, y) = x tany + ye-2*, find and What do you notice? дхду (b) If f(x, y)…

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Q: 5) y"-y'-2y=x+cosx

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Q: 26. da (x² cos y+ sin 2y) =(ry) x(- sin y y') + (cos y)(2z) + cos 2y - 2y = x-y' +y·1 = %3D %3D dx…

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Q: 7- y" + 4y = cos x, y (0) = 0, y(n) = 0

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Q: 2. The position vector of a particle is given by r(t)= (2 cos t sin t)i +(cos^2 t - sin^2 t)j +…

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Q: Consumer Reports rated airlines and found that 89% of the flights involved in the study arrived on…

A: This question is of statistics

Q: Find y' where y = tan(11a? + 8) v173 + 17 Answer: 51a2 y/ = sec2 (22æ)\/172³ + 17+ tan(11a² + 8)…

A: I have used the rule for composition of function and multiplication of functions

Q: If r(t) = = cos(-3t)i + sin(−3t)j – 10tk compute r' (t)= i+ i+ (cos (-3t))/3 and fr(t) dt= (-sin…

A: r(t)=cos(-3t) i+sin(-3t) k-10tk

Q: Find the general solution of the system of equations 2 -5 x' 0 = - ( ² = ₂ ) x + ( cost), 0 < t < *.…

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Q: 1. If f(x, y)=3x' cos y– y sin x– 2.x In y- yln x-4x²y, find ôf ôf d²ƒ _ô²ƒ

A: According to question given thatf(x,y)=3x3 cosy-y2 sinx-2x ln(y)-y ln(x)-4x2y

Q: (4) M" - afg' -4fg= 0; Y@-1, g'()=0

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Q: a) Use the Euler formula, e¹⁰ (cos(0) + i sin(0))" = cos(n) + i sin(n). b) Suppose y(t) = e-2t eit…

A: In this question, we will find the solution to the given problem.

Q: Suppose that ye cos Bx is a solution of y-y +ay -9y =0 where a and B are real constants Then the…

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Q: valuate the integral using U-substitution x dx (7x2+3)5 1) S A)-(7x²+3)-6+ C C)-(7x² + 3)-4+ C…

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Q: x' - x? = t, x(0) = -2, 0, 2; x(2) = 0; x(2.5) = -3, 0, 3 7. y'= sin(yx), y(0) = 0.5, 1,1.5, 2, 2.5…

A: We will use Mathematica to solve these. Each question has multiple initial value problems. 6 (a):…

Q: d du 1) (sin-1u] dx %3D 1-u2 dx -1 du 리는 [cos-1 ul = dx V1-u2 dx d 1 du 3) = [tan-1 u] dx %3D 1+u2…

A: I have solved first three part for other repost question

Q: sin 8- + jG+1) sin² (@) = k² (27) sin e. and, (28) Z dộ? Show that equation (27) combined with…

A: given equation 1TsinθddθsinθdTdθ+jj+1sin2θ=k2        ...27 and 1Zd2Zdϕ2=-k2       ...28 use equation…

Q: 4) Find ôw/ ôr if w= (x+y+z)*, x=r-s, y = cos(r+s), z = sin(r + s) the point (r,s)= (1,-1)

A: Given - w = x + y + z2 , x = r - s, y = cosr + s, z = sinr + s To find - Find ∂w∂r at the point r, s…

Q: Solve J²u = Ət² u (0, t) = u (x, 0) = J²u 4- 2 მ2 u (π, t) = 0 sin (2x), 0 0 (x, 0) = 0 Ju Ət

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Q: 2) (3x²y+ 4e)dx + (x³ + 4xe + 2y)dy

A: We are authorized to solve only 1 question, please repost remaining questions Differential equation

Q: 36. Find the critical points using second derivative test of the equation y = 2x³ + 9x² + 27 %3D a.…

A: This question is related to derivatives.

Q: The general solution of (D²-2D+1)y=2sin x A) y=ce*+C2xeX+sinx B) y=c1eX+C2xex+cosx y=C1eX +C,XeX…

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Q: not Show that ([0,1]_is in the l' metric d (fig)= (51f6)-96) ³d x) ² fumpluts

A: The given set is X = C[0,1] and the metric defined on X is L2 metric which is defined as  df, g =…

Q: 7. Find the general solution of (Dʻ + 2D’ + 10D²)y = 0.

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Q: y= (12,4 + x)* + (1+)(Va² +x- c )cos²(4x), c)cos²(Ax), 3)4( 3 y = (12,4 +x)* + (1+x' Зx +x — с y = ?

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Q: The equation (tan²x+3y²)sec²xdx + (3tan²x + y²)dy=0 can be solved by

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Q: x²e*= sin(x² yz) Let f(x, y, z) %3D 12 o f find dydzd' x at the point (2, 0, 0)

A: Expanding the terms as power series then differentiating

Q: In implicit differentation problems it seems we treat x and y differently. For example, when we…

A: Recall: Chain Rule of differentiation :    If F(x)=f(g(x)) then ,   F'(x) = df(g(x))dx =…

Q: Part 2 HW5 Find a sequence that has a subsequence converging to a limit which is not the limsup and…

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Q: -2x Use Green's Theorem to evaluate [(3 ye^²* − 7 sin² (3x³)) dx + (5x² + 2x²y² +8e³¹²-7x+²) +2) dy…

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.