Solve each of the following equations. 1.y( x² – y + 1) dx + x( 3x – 4y + 3) dy =o 2.Siny (x + sin y) dx + 2 x² cosy dy=D0

Q: (b) sinr + cos² y 4 P(품,등) 3

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Q: [2x + y cos(xy)]dx + [2y + x cos(xy)]dy

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Q: d²y Find С. dx? 1. y= sin 2x +cos² x sin x 2. у- - y= 1-cosx

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

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Q: 3. Verify that ysin x-xy =0 is a solution of the equation y(cosx-y)dr+(sin x- 2xy)dy =0.

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Q: 2. Obtain the general solution to the equation dy dx x sin x y cos y

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Q: Which of the following equations is NOT an exact equation OA. (2x sin y + y)dx + (x² cos y + x)dy =…

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Q: Which of the following equations is NOT an exact equation?| OA. (2x sin y + y)dx + (x² cos y + x)dy…

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Q: sin? 2t and x = cos² t

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Q: Solve each of the following equations 1. (2x – y+ 1) dx + x(3x – 4y + 3) dy = 0.

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

Q: Which of the following equations is NOT an exact equation? A (2x sin y + y)dx + (x² cos y + x)dy = 0…

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Q: Given the following DE (cos 2y – 3x?y?)dx + (cos 2y – 2x sin 2y – 2xy)dy = 0 -

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Q: dy dx = general solution of :- - 2 Sec 3x tan 3 X

A: dy/dx=sec2tan3x

Q: 2x³y = y(y? + 3x?). 4.

A: The given equation is 4) 2x3y'=y(y2+3x2) 5) (2x-y)dx+(4x+y-6)dy=0

Q: Find the general solution of the following equations? y" – 3y" – y + 3y = 2x + 40 sin x 3-

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Q: dx 6. [- xIn x sin 5tdt 7. V1+ cos 5t

A: Given that the integral ∫dxxln2x. Give suitable substitution to simplify the integral. Let u=lnx,…

Q: 2 X 1 t3 COS 4- x² dx 2 -2

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Q: (4e²+7x°+5 cos z + 2)dx

A: Solve integration

Q: S cos(3x – 2n) cos (x + t) dx

A: We know that, 2cosAcosB=cos(A+B)+cos(A-B) Also, ∫cosxdx=sinx

Q: Differential Equation: y'(t) = y2(2-t) Find the isoclines of slope zero. Sketch solution curve…

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Q: d²y 9. +y= sin 3x cos 2x 2

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Q: cos 2y dy sin y

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Q: 1. y-y-3y = sin 2x

A: we have given differential equation

Q: Which of the following equations is NOT an exact equation? O A. (2x sin y + y)dx + (x² cos y + x)dy…

A: The given differential equations are: A. 2xsiny+ydx+x2cosy+xdy=0 B. 1ydx-xy2dy=0 C.…

Q: So S6 x²cos(xy)dxdy

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Q: 2. Solve dy dx = e 5x + sin 3x + 2x; y(0) = 2

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Q: d 1. Evaluate: dx [V5 5+ (x° + 1)³ d cos* x + sin* x dx 4 4 2. Evaluate:

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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.