(x² + 2x + y) dx + 2dy = 0

Q: dx x2 - 2x + 82 ||

A: Formula used     ∫  1/(u^2+1) du = tan^-1(u) + c

Q: f(3x² cot 2x³ csc 2x³) dx O-csc 2x³ + C CSC O csc 2x³ + C Ocsc 2x³ + C CSC O-csc 2x³ + C

A: We can solve as follows

Q: Find x and y if (-3x - 9) + 4i = 6 + (3y - 2)i.

A: Given that,  (-3x - 9) + 4i = 6 + (3y - 2)i To solve for x and y, need to use below property of…

Q: (4D4 - 4D3 - 3D2 - 2D + 1)y = 0

A: We have to solve the given equation.

Q: 2x+2 y = 5

A: Given : 2x+2y = 5x+y = 3

Q: 2x +4y-2= X -y +2 =-6 3x +2y-Z= 5

A:

Q: 1. dx x2 + 6x + 10

A:

Q: Write y=2(0.5x-6)(6-24x) in the form y=k(x-r)(x-s) and give the values of k,r,s.

A: We have to factor out 0.5 and -24

Q: Integrate: 22 3 + 2x + 10 - dx

A:

Q: Integrate dx Vr® + 4

A: Given integration is                                                              ∫x2x6+4dx here we…

Q: X2 dx ex+3

A:

Q: is y=3x+4 a direct variation?

A:

Q: find x and y if (2x+1,y)=(5x+4, -7)

A: Given: 2x+1,y=5x+4,-7

Q: 7 x2 dx + 4x + 20 13

A:

Q: dy +y%3DX² 2.

A:

Q: Find the characteristics equation of x²r+2xys+y²t

A:

Q: (4x² – 5x)5(8x – 5) dx

A:

Q: Find: 6x 3x2-7x+4 dx ---

A: An integral is given as, ∫6x3-3x2-7x+4dx. The objective is to solve the integral and find the value.

Q: 2. Write the program to find Laplace inverse for this equation: 4 s+ 5 Y(s) =& - 4)°(s+5)l %3D

A: The linearity property of Laplace transformation is,  L-1a·fs+b·gs=a·L-1fs+b·L-1gs And,  L-11s-a=eat

Q: x - 3y = 1 2x – y = 7

A: Our Aim is to solve the given equations below:-x-3y=1 -(i)and 2x-y=7 -(ii)

Q: 4x+12 dx -36 (#4) |

A: Taking 4 common outside from the numerators term, The denominator can be written as

Q: Solve 3x + 2y > 6 graphically.

A: Shaded area below is the graphical solution.

Q: 3y +5 (5y-7)2 dy

A: We can find the integration as below.

Q: 4x-2 dx 27x-8

A:

Q: 2 15х? -13 dx - 14х За +2

A: We will apply long division to solve integral

Q: (3x/5y) (y2/6x)

A: The given expression is                                     3x5yy26x Now we simplify this given…

Q: d²y if 2x²-3y²=7 dx2

A: Differentiating both sides of the equation. 23x2-32ydydx=06x2-6ydydx=06ydydx=6x2dydx=x2y . . . . . .…

Q: (24+2x-x2)1/2dx

A:

Q: Express 2e3+in6 in rectangular form.

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Q: f 12x -9x +2 dx 3.

A:

Q: 2y = x + 1 -2x - y = 7

A:

Q: (3z² + 1) dx (2 + 2x + 1)²

A:

Q: Find y" 4x + 1 y%3D %3D 2x

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Q: (x² D² - xD + 3) y = x²(Inx)4

A:

Q: y=4x-x², y=x

A: