A particular solution of x²y" - x(x + 2)y' + (x + 2)y=2x³, x>0, V₁(x)=x, V₂(x)= xex 2x²+x a. b. -2x²-x C. - 2x² + =—= 1 d. e. O O a O C O D -2x² 3²

Q: Solve for x, y and z x + 2y - z = 0 2x + 3y - 2z = 3 -x - 4y + 3z = - 2

A: x+2y-z=0            i2x+3y-2y=3        ii-x-4y+3z=-2    iiii+iii-2y+2z=-2⇒-y+z=-1…

Q: If roots of x³ + 5x² – 7x – 1 = 0 are a, B, Y then the equation whose roots are aß, By, Ya is- (1)…

A: To find the cubic equation with the roots as aB , Br and ra

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: {3x+y=-3 2x+3y=5 (X,y) =

A: Given: 3x+y=-32x+3y=5 To Find: The value of x,y.

Q: 2x+3 a) S; dx x2-3x+2

A: We integrate the following by using substitution rules and factories the denominator.

Q: Find the general solution of a = y+2x. O a. y = -z(Inz +c) O b.y = a (2ina +e) O c.y = a(2ina +c) O…

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Q: Find the values of x and y for which (x + y, 0) = (3,1 - y)

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

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

Q: · (D² + 3D + 2)y = xsin 2x

A:

Q: max-2x1-x²-x3 s.t 1 + 2x2 + x3 = 1 4x1+3x2+2x3 1, 2, 3 > 0 = 2

A: We have to find the maximum value of fx1, x2, x3=-2x12-x22-x32.Subject tox1+2x2+x3=14x1+4x2+2x3=2x1,…

Q: Eliminate the arbitrary constant. y=Ax² + Bx³ 7xy "-x²y + 15y = 0 A (В) B (C) D x²y-7xy "+ 15y = 0…

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Q: 5. Solve IVP у" - 4y" + 7y - бу %3D 0, у(0) %3D 1, у'(0) — 0, у" (0) — 0

A: See the attachment

Q: Lt² V4-t² dt V(4-x)/(2\x) x(4-x)

A:

Q: If  x3 + y3 = 30, x+y =6, then 1/x+1/y = ?

A: We need to find,

Q: Find (4z² + 3z")dz -1

A: In this question, we need to find the integral of the given function.

Q: y(4) + 3y" - 4y = 0

A:

Q: Resolve yDx-2(x + y)Dy = 0 O x² + 2y = cy² ○ x + 2 = cy² O x + 2y = cy² Ox+2y=c

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Q: 2 x²+yi -I -VI-2²

A:

Q: Find a general solution of y"=(-2+2isqrt(3))y

A: Given that, the differential equation is- y''=-2+2i3y On simplifying, y''--2+2i3y=0

Q: 9) (4y? + 10xy – 4y + 8)dx + (2x² + 2xy – x)dy = 0 ; when y(0) = 1 %3D

A:

Q: 1) 2x+8y=20 y=2

A: 2x+8y=20..................1y=2.............................2

Q: Verify that y = + C2x + C3xlnx + 4x² is a solution of x³y"" + 2x²y" – xy' + y = 12x²

A: Given y = C1x+C2 x+C3 x lnx +4x2y' = -C1x2+C2+C3 lnx + C3+8xy'' = 2C1x3+C3x+8y''' = -6C1x4-C3x2

Q: x = (1- y)*(3y +1) ;y"

A: Answer is given in next step.

Q: solve for 1, x = 2x² – 5x + 2, z = - (x+t) - (x) t

A:

Q: Ex.: Solve (2D+3D-9)x+(D² +7D-14) = 4 (D+1)x+(D+2)y= 0 (2)

A:

Q: I-1 I 1² +51 +8 dz

A: Given, ∫x-1x2+5x+8dx