The general solution to the DE y =2x +y-2 is (Hint: use the substitution U=2x+y). O y=/2x+y-2x+c O 2/2x+y=Dx+c O 2x+y-y%3Dx+c O None of these O V2x+y-2xy=Dc

Q: Integrate S(csc 3x + cot 3x)²dx A. cot 3x –csc 3x –x+ C -cot 3x -csc 3x – x+C -를cot 3x- sc 3x + x +C…

A:

Q: If y = C1 + C2x +e2*(C3cosx + C4sinx), then the roots are

A:

Q: If the substitution u = √x + 1 is made, the integral 3 A S u² u² - 1 du B du 3 2u²2 u² - 1 √ √x+1 dx…

A: We solve the given problem by using the substitution method.

Q: dy if y= 3x Find dx х2+1 3(1-х2) D) (x2+1)2 3x2-3 A) 3. 3 B) 2x C) (x2+ 1)2 х2 +1

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Q: Suppose x² y² = x + 17y x = y Find 17 x + y x² + y² + 1

A: Given that, x2=17x+y, y2=x+17y, x≠y Find the value of x2+y2+1. As we know the formula: a2-b2=a-ba+b

Q: ntegrate: 16x³ + 64x² 7x +41 16x² +9

A: ∫-16x3+64x2-7x+4116x2+9dx Lets first divide using long division.

Q: 2 c4 e-x-2y dydx 2х

A: It is double integration problem

Q: 3. y = x2 - 2 -3 -2 -10 3D 2 3 X

A:

Q: S,(2x-y)dxdydz

A: Consider the integral: ∫12∫0z2∫0y-z2x-ydxdydz

Q: Question 2. Is the collection F of all polynomials p(x) with p(3) polynomials? = 0 a subspace of P,…

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Q: Is the ordered pair (4, 7) a solution to which equation O 3x + 4y = 4 O 3x = -4y+ 4 O y = 3/4x + 4…

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Q: 1 4. (1+2)y/ + 2ry = (1+2)y

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Q: 7x+1 + 3x 4y y 6. x+1 3x-7 7. 6x 3x 5y 8. 9y+4 2y+1

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Q: 2 Ⓒz² = x² + y² 2

A:

Q: =D5 -3x+4y%3D8

A: y=5 -3x+4y=8

Q: Evaluate [ T 1-x² x² + y² dydx.

A: Given: The integral is ∫022∫x1-x2x2+y2dydx. The aim is to evaluate the given integral. Concept:  The…

Q: 1 √x y³+1 2 Sőt. S²/E 0 dydx

A: We are given an integral. Our aim is to evaluate the integral ∫04∫x21y3+1dydx.

Q: ind the value of x and y given that X. - 24 3 土 %3D 2 -2x 4 -5

A:

Q: Kindly exhibit that xzxx+yzxy=y2zyy if z=xy+yln(xy)

A: The given data is: z=xy+ylnxy To prove: xzxx+yzxy=y2zyy

Q: If 2x = xy + y2, then A. C. -2 + y x + 2y (2-y) x + 2y dx 11 B. D. -(2 + y) x + 2y -(-2+ y) x + 2xy

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Q: dx = 2x - 1 x³+3x + C x2 +C -- 3+C 2. 6. In x +C In x +C

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Q: If W = 2x 2 + 3xy2 - 20y-2+ 6u; where x = 5u2 +4v 2 and y= u - 4v3 , find §W / §V.

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Q: Evaluate ſ / 21 + 12x – 9xr“ dx -

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Q: Find xy² Una -dA, R= [0,4] × [-2, 2] x² + 1

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.