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

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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: y = √√²+csc²(πx) 2 COS os(3 cos-¹(x)) - a X

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Q: Exercises (11): Find y if 5 1. 1 -1 y = xcsc 1- x2 sin (x + y) = cos'xy 2.

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Q: sin? 2t and x = cos² t

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Q: g" - 3 y" y" they = +4y - 23 2 cos x 20

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Q: |( + 3t) sin(2t) dt 13.

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Q: (3x² – 2xy+ y²) dx + (2xy – x² + sin y) dy = 0, y(12) = 0 - |

A: We have to find the required solution of…

Q: + 3r?y – y³ = 4, find dx Given sin

A: Given that sin (y^2/x^2) + 3x^2y - y^3 = 4. We have to find the value of dy/dx.

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

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Q: Which of the following is a solution to x² + 3x - 3y = 0² dx² dx a.y = 8 b. y = 2x c. y = ex d. y =…

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Q: 3. Integrate the following: 2x+3 i. J7+3x ii. S V1- cos x dx iii. S cos3 x dx

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Q: du = 3 and dx dy = cos u, find the du dy Given y = sin(3x – 2). If dx 3 cos(2x) 3 cos(3x) 3 cos(3x –…

A: Topic:- derivatives

Q: sin y(x + sin y) dx + 2x² cos y dy = 0.

A: Given equation is  siny(x+siny)dx+2x2cosydy=0

Q: 5. (2x – y) dx + (4x + y – 6) dy = 0.

A:

Q: ca/4 4. +1 x cos y dz dx dy

A: Triple integral

Q: 4: Find aun -2 2y² Sin(xy) dx dy

A: Topic:- application of integration

Q: 1 1. (3xy + y²) + (x² + xy) 4/2 = 0 {x³y + x² y² = c} dx ― 2

A: Given differential equation

Q: (4e²+7x°+5 cos z + 2)dx

A: Solve integration

Q: x+y) d

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Q: 3x d. Evaluate dx COS cos (3t – 1) dt

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Q: d²y 9. +y= sin 3x cos 2x 2

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Q: 2. (2y? + 3xy – 2y + 6x) dx + x(x + 2y – 1) dy = 0. -

A: Follow 2nd and 3rd step.

Q: (2xy-3x²) dx + (x² + 2y) dy = 0 2

A: Given differential equation:- 2xy-3x2dx+x2+2ydy=0

Q: B. 1. 2. 3. Find dy for the following equati dx X²+y²2-2x+3y=0 1 = 4 x² + y² x³+y³+4xy=5

A:

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.