If y = f(x) is the solution of (18x?y + 2x)dx + (6x – 108y?)dy = 0, f(0) = -1, then Lütfen birini seçin: O a. f(6) = 4 O b. f(6) = 6 || O c. f(6) = 5 O d. All the previous answers are not correct. O e. f(6) = 7

Q: Solve for the value of C in the equation: (3xy² + 2y)dx + (2x²y + x)dy = 0 when y(1) = 2 OA. 4 O B.…

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Q: Evaluate. 5 - 3 (7x + y) dx dy 0 - 4 5 - 3 I (7x+ v) dy dy i (Simplify v

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Q: (D2 + 5D + 4)y = 3-2x, Find Yp O a. 11 O b. 00 8 | O d. 11 8 X 11 X 8 3 OC. 11 X + 3 8 3 O e. none X…

A: SOME TERMS ARE EXPANDED BY USING BINOMIAL EXPANSION WHICH IS AS FOLLOWS-:…

Q: 1o 5. If p l/q, 4 = 12x- 6, and 21 = 14x+ %3D %3D work? 3/4 1/2 5/6 .

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Q: b=? The following equation is exact if (bxy²+4)dy=(7x-4y³) dx O 12 O-12 04 O None of the others -4

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Q: Solve (2y+5)dx = 6dy O a. y 3ln(2x +5)+ c O b. x 12ln(2y +5) + c Ocx=3In(2y+5)+c O d. x == 21 In(2y…

A: The given differential equation is 2y+5 dx=6 dy. Solve the given differential equation as follows.…

Q: 7) A building is 300 feet tall. It casts a 165 foot long shadow. A statue near the building is 40…

A: Given: A building is 300 feet tall. It casts a 165 foot long shadow. A statue near the building is…

Q: S¹₁₁ S1+₂x² x + 2y dy dx ·12x²

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Q: A. Obtained the general solution. E... 10. (D² – 3D + 2)y = 3x²

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Q: 1 S dx = 3x+2 0-²(3x + 2) + C O 2√3x +2+c 3 O²(3x + 2)² + C A O√3x + 2 + c

A: The given integral is: I=∫13x+2dx  ...1   As we know the Power Rule: ∫xndx=xn+1n+1+C ; n≠-1

Q: dy 6. dr = (2 +y + 1)2

A: The given problem is to solve the given ordinary differential equation, we can solve by using…

Q: -1 dr =? x2 + 4x + 5 O A 3T 2 D. 37 4. B.

A: Solving the improper integral we have

Q: 1 1+x2 (y + 2x)¯i dy dæl 0 0

A: Double integral

Q: d Find [In(x2 + 1)] dx 1 b. x +1 2 2x c. а. x+1 x +1 d. 1

A: We need to find the differentiation of the given function.Below find the solution in the image.

Q: (D² + 5D + 4)y = 3-2x, Find Yp O a. 11 8 O b. O C 1 11 O d. 11 8 11 8 3 8 + X 3 e none I + X 3 X X 3

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Q: Find y if In X Jer X (2x + 7) dx +4% + +4x + 8 8 | + ² tan y + c

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Q: Solve for the value of C in the equation: (3xy2 + 2y)dx + (2x²y + x)dy = 0 when y(1) = 2 O A. 4 B.…

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Q: If 2y - 3x = 5, then at (-1,2) is O a. -3 O b. 3 Oc. O c. -3 O d. 6 614

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Q: B D E 2x None 2 A √ N dx is equal to

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Q: x3 dx= 9- x2 a. None of the other answers are correct. b. 3 9 – x² - 27- /9– x² +C 3 3 27 (x 4 +C 3…

A: To evaluate the integral: ∫x39-x2dx Solution: Let t=9-x2. Differentiating both sides, we get…

Q: x2 +3 dx x (x2+2x+1)

A: This is a question of indefinite integrals.  To solve this question we will apply the concept of…

Q: 2х + 3 dx Vx + 2 J 3 4 Answer: (x + 2)7 – 2(x + 2)7 + C

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Q: 3. If c (5x+ 2) = dx - 3 then the solution for x in terms of c and d is 3+2c (1) Sc -d 2cd (3) 5c-3…

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Q: I have a question with regards to a. In the step where the substitution of the values happened why…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: dz 4. Let r - y – 23 = 6ryz, then the value of is dr %3D 22 + 2ry (d) 코- 2yz 2 + 2yz y? – 21z (c) 22…

A: We are given: x3 -y3-z3=6xyz we need to find the derivative of z with respect to x. This can be done…

Q: (D2 + 5D + 4)y = 3 - 2x, Find Yp O a. 11 8 O b. O C. O d. 11 8 11 8 11 X 8 3 + X O e. none 3 + X 3 X…

A: Given , (D²+5D+4)y= 3-2x So, yp=1/(D²+5D+4) {3-2x}

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.