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: Verify whether y(x) = 2e-*+xe-* is a solution of y" + 2y + y = 0.

A: Topic = Differential equation

Q: Q4: Use undetermined coefficient annihilator approach to solve. y"" – 5y" + 6y' = 10x² – 5x – 6 +…

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Q: Solve the given equation.. (3x²y + 2xy+y³)dx + (x² + y²)dy=0

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Q: 1) S dx 9-x2 dx 2) J2y-2 x2Vx2 -2 3) dx 2 V1-x2 |3D

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Q: (1+ ye" + xye")dæ + (xe² + 2)dy = 0 C = xye² + 2y+ x C = xye" – 2y – x %3D - Option 3 O Option 4 C =…

A: ANSWER: Option 3.

Q: A/If x² (y - 4z) - y²(2x + 3z) + z²(3x - 4y) = xyz Find Zx

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Q: u" - 16u = 0

A: Given the differential equation is u" - 16u = 0. Here the auxiliary equation is m2 - 16 = 0

Q: Find the general solution x²y" - xy + y = x lnx

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Q: Find the solution of 4x²y" — 4x²y + y = 0, x > 0 of the form Y₁ = x¹(1+c₁x + С₂x² + c3x³ + ...)…

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Q: Reduce the equation yzxx + (x + y)2xy + XZyy = 0 to a canonical form and solve it.

A: The characteristics integrals:

Q: Solve using variation of parameters or reduction of order (D² – 3D + 2)y = (1+e²x)¯2

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Q: d?y dx3 Solve - 27y=0 O a. y = ce -3x + e7*(c2cos- 3/3 x+C3sin 3/3 -x) 2 Ob. OBy=c,e3x +e"(c,cos 33…

A: We have to solve given problem:

Q: 3. Find the general solution of 2ху? + 4 %3D 2(3 — x?у)у'. А. X2у2 + 4х — бу %3D С B. x²y? – 4x – 6y…

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Q: Solve the equation (x + 2y-4)dx - (2x + y - 5)dy = 0. (x + y - 1)² = c(x-y-3) (x-y-1)² = c(x + y -…

A: x+2y-4dx-2x+y-5dy=0

Q: Solve the Cauchy euler equation 3x2+ 6x-6y = 3 + Inx d²y + 6x2-6y = 3 + lnx³ dx3

A: In the given question we have to solve the given Cauchy Euler equation. Method: the Cauchy Euler…

Q: Let 1 2 -1 A = 2 4 -2 -2 Describe all solutions of A = 0. * = x2 +x3 +x4

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Q: 1 Find the solution to (2x+3) y'=y+ (2x+3) ²; x = -1;y=0 1 2y = (2x+3) 2 In (2x+3) In(2x + 3) 3 y=…

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Q: In(-/-) (vi) 2x In - x = 0

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Q: Q1: If y" + y = x², then yp = Q4: The solution of y(4) - 5y" + 4y = 0 is: (B) c₁e* + c₂ex +…

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Q: DETERMINE SOLUTION OF 1 x dy dx + y = x² + x (2x+3y-13) dx + 3x - 2y) dy = 0 DE

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Q: -1 -1 3. Find a particular solution of x' = -2 2 x+ 4 -1 -2 et

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Q: Find two linearly independent solutions of 2x²y" - xy + (-4x + 1)y=0, x > 0 of the form y₁ = x¹(1+…

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Q: y₁=1+a3x³ + arº +... Y₂ = x + b₁x¹ + b₁x² + ... Enter the first few coefficients: a3 = a6 = b₁ b7 )…

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Q: Which of the following is the general solution of x 2 V) 2 -xy'-56x 2 =0? O a.…

A: We have to solve given problem: Note: given differential equations is wrong. According to options…

Q: Select all equations that are equivalent to a-6z 16. a + 6x 9 0 O b a + 6x +9 = 16 Oc a+6x + 9 = 25…

A: Solution:-Given equation,     x2+6x=16  —1let us see and solve each option given,a…

Q: dy x+y+1 5. dx 2x + 2y+3

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Q: Solve for the general solution * (4xy+3y – x) dx + x (x + 2y) dy = 0 x' (4xy² + 4y – x) = c x²…

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Q: 7. (x+2yXdx- dy) = dx + dy. %3D

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Q: (3 + a?)y" + 3y = 0, y(0) = 0, y'(0) = 7. %3D If the solution is k=0 enter the following…

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Q: Solve the Cauchy euler equation d²y + 6x 2-6y = 3 + Inx3 dx x3 d3y 3x2 dx2 dy dx3

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