D. Verify if The relatum O y= xe' y= eco{ 2x) is a soluhon to yl-Gy'+13y=D0 is a solution to yl - 2y'ty =0. %3D

Q: 1. Solve Cauchy-Euler equation. r²y" – ry' + y = 2x

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Q: A. Determine the Degree, Order, Unknown Function and Independent Variable * d²x 1. y dyz = y² + 1 2.…

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Q: D. Exponential shipting Theorem (D°+ 10* - 30 - 18) y = 24 x ° e-s* -3x 4.

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Q: 5. y" + 3y" + 4y' + 12y = 8cos2x – 16sin2x

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Q: Double root. If D2 + aD + bl has distinct roots u and A. show that y = (e"* - e^./H ). Obtain from…

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Q: find sol. y'- y =y2e-x

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Q: Solve the following DE using variable separable 1. dyidx = 4x + xy/y -xy

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 4. Solve the following DE: (2x²y)y' = x³ + 2y³

A: Given in the question, The diffrential equation is as follows:- By dividing both sides by 2x2 * y3,…

Q: 2. Use Method of Undetermined Coefficients: y" - 2y' + 5y = 4e*cos2x + n IN

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Q: -2dх 38. y-2dx dy er e2x + 1' УО) %3D 1

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Q: (D² – DD' + D)z= 1 1- Solve

A: Here the given equation is non homogeneous partial differential equation with constant…

Q: Solve: dy dr = y +e*y?

A: The given differential equation is dydx=y+exy2. Rewrite the differential equation as,…

Q: -3x у" + 5y' + 4y %3D 10е'

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Q: Is the equation separable, linear, bernoulli, or homogenous? dy а. dx x4 + 4xy² 2x3 + x²y +y³ b.…

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Q: 2. y" - 3y' +2y = e4x + 6x³ – 2+ 3sin(4x) | |

A: See 2nd step

Q: 2. Use the Trope zoid to estimate the' valve the integral numerically. Give your final se the Trope…

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Q: 5. (x + y)dy – (x – y)dx = 0. %3D

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: Verify that y = x² – 1 is a solution of (y')* + y² = -1. %3D

A: Given;            y=x2-1 is a solution of y'4+y2=-1 We compute the first derivative.…

Q: 3. Solve (2xy – y² + y)dx + (3x² – 4xy + 3x)dy = 0. (Non Exact) 4. Solve the following FOLDE: (2у +…

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Q: Solve by finding an I.F 1. xdy – ydx = (x² + y² }£x y - sin x 2. dy + -dx = 0 ......

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: 2. y" + y' = cscx %3D

A: 2. we have  y''+y'=cscx  first find C.F m2+m=0m(m+1)=0m=0,-1y(x)=c1e0x+c2e-x=c1+c2e-x

Q: 5. Solve the D.E. y" + 4y = e-*.

A: As per our guidelines we are suppose to solve only first question. Kindly repost the other question…

Q: 2. * Evsluate O 4 | dx Evoluate @ 12-X

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Q: d) 3xy" +4y' +y = 0.

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Q: 5. Solve the IVP: 2 y' +y= -x°y5: y(-1) = 2 A. 16 = y (32x10 - 31x") B. 16 = y*(32x!0 +31x8) C. 16 =…

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Q: Solve the non-homo . D.E. 1.y" + у %3D Зе2х

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Q: 9. Calculate y' for y +2xy = 3x-2y %3D

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Q: 1. y = x3 – 2x² + 3x – 5 - - dy 3x2 – 4x + 3 - dx

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Q: Find dy if x2 + 6xy = 3y2

A: Given: x2+6xy=3y2 If function if f(y) then differentiation w.r.t x is ddxf(y)=ddyf(y)dydx

Q: 4. y"+2y'+2y=e* cos x 3t 2.x"-2x'–4x = 2e" 27 6. x"-4x'+4x= te" %3D 5.

A: See the attachment.