dy Solve the DE. x +x = sin (x + y) dx

Q: Given y= 5e3X + sin x, -is dx A) 5e3x + cosx B 5e3x – cosx 15e3x + cosx D 15е3х — сosx

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Q: dy dzy B) Find and if x = sin? 3z and y = tan 3z dx dx2

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Q: 3) eYsinx dx = cos?x dy 4) y' + (÷) y = xy?

A: First question we can easily solve using veriable separable method. Second question we can use from…

Q: 4X dy 2siny ?) S dy sinzx e 3) S sin? dx

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Q: Determine the particular solution to dy/dx= 2 sin x, y(pi)=-2

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Q: j) S (2 cos a – e) dx

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Q: T/2 e2x sin x dx

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Q: Use the variation of parameters to solve the following equation: d^2y/dx^2- 3 (dy/dx)+2y=cos⁡(e^-x)

A: I am attaching image so that you understand each and every step.

Q: d²y dy and - dx B) Find if x = sin? 3z and y = tan 3z dx2

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Q: Solve the given DE: dy ex – 2x cos y ey – x² sin y' - dx

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Q: d'y dy tion dx? + sin x = 0 is + y- dx

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Q: The solution of the DE dy + (y – 1) dx =0

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Q: solve the DE b

A: The DE is (x-y+2)dx-dy=0or, (x-y+2)dx=dyor,dydx=x-y+2

Q: dy d'y dx ' dx? 2. If y = sin 2x – 2 cos 3x,the find, at x 0

A: The given function isy=sin2x-2cos3xto finddydx, d2ydx2    at x=0

Q: S*r(sin³x cos x + sin x cos x) dx -- 4 Ja sin 50 de

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Q: cos ax -dx = re¯ª,a>0. .2

A: With the help of Residue we can prove given result:

Q: Solve the first order inhomogeneous equation dy + 2y = 3x2 dx Hint:

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Q: dy Solve Y for y=/4×(sin x) cos dx

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Q: dy cos?x = -(tan x)y ;y(0) = -1 b) Solve %3D dx

A: Given that: dydx-cos2x=-(tanx)y; y(0)=-1

Q: VE-1 x= sec?t b) Find for y = dx sint

A: y=t-1sintDifferentiate w.r.t 't'dydt=sint·12t-1-t-1…

Q: 1 y Solve the integral: cos -dy dx - T/2 Jo

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Q: Show | S a² sin®(e*) dæ| < 16n*. 8 Show | S, x2 sin°(eª) dx| < 3

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Q: d²y Answer: 1 . If x = t + cos t, y = sin t, find dx2 dx2 (1-sin t)

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Q: 14. Solve the equation d?x dx dt +2x sin 3 dr? dx given that at t= 0, x = 0 and %3D dt ment

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Q: dy x2 (b) Find the general solution to the DE cos? y dx

A: As per our guidelines only one question can be solved. Solution for "b" is given below in the next…

Q: dy Find dx 1/4 | sin (?) dt y =

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Q: dy = 6x– 2x + 1 cos y + eY %D dx

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Q: dx 27 (d) 2 + cos (x)

A: As per bartleby guidelines we are supported to answer only one question at a time . Kindly repost…

Q: The appropriate change of variables for the dx is Vx²-4 x=2 cosØ O x=2 sec Ø O x=2tan Ø O x=2 sineØ

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Q: Solve the DE (ey+1)cosx dx+eysinxdy=0

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Q: 4 dy 5. х dx + бу %3D 3хуз 3xy

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Q: = cos?y is dx The general solution of the DE

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Q: (c) [ e sin(x²) dx < e –1. Show that

A: Solution of question as follows

Q: 3) I = dx 4) 1 = S cos?x dx

A: Given that

Q: Q) Find the general solution. dy sin-1x Iny dx II

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Q: d’y Find dx? 2 2 1. y = sin 2x +cos x

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Q: 24. x² sin y dx dy

A: Given :   ∫-11∫0πx2 sin y dx dy=?…

Q: The general solution of the DE dx dy = cos?y is

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Q: Solve the following Bernoulli equation. (* – 2xy dx + 3x²dy = 0 where y(2)=1.

A: Given, The Bernoulli equation y4-2xydx+3x2dy =0   Where y2=1 We have to solve the bernoulli's…

Q: Solve the DE by Bernoulli's Equation 3 1.6 y² dx - x (2 x³+ y) dy = 0

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Q: (ei-e) dx +x cosh udu = 0 when x = 0; u = 0 1. %3D

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Q: Find the general solution of the following equations? dy 1- x². x2 + sinx – y = 0 dx

A: Given differential equation is

Q: evaluate the triple iterated integral.

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Q: Solve the given DE: dy e* – 2x cos y eу — хx2 sin y' dx ||

A: Differential equations is solved.

Q: d’y dx? Find the general solution for +10 -+25y = 0. dx

A: For the second order homogeneous differential equations of the form ad2ydx2+bdydx+cy=0 , the general…

Q: Solve the given DE: (yexy + cosx)dx + (xe*y)dy = 0.

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Q: dy Solve cos x(e2y - y) - dx = e' sin 2x,

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Q: L, 4x(1– x²)dx S 2 i) ii) -) dx ? (х + Sin?x

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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.