Obtain the general solution C. (D2 + 2D + 2)y = e-x

Q: Q2) The general solution of y" + 2y"-y' - 2y = 0, is: a) y(x) = c₁e²x + ₂x + c₂e* c) y(x) = c₁e²x +…

A: Solution :-

Q: ² - x ²² = y² dz ४x d²z Find the solution of xy' буду

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Q: Solution of the D.E y"+ 3y' + 2y= 12x² when solved using the method of undetermined coefficients is

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Q: (D² + D)y =x+| ;

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Q: If y = f(x) is the solution of y' – 3y =-12.e 9z, f(0) =1, then

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Q: The general solution to D. E 2y(4) – y'"" – 2y" + y' = 0 - is given by y(x) =

A: The genaral solution to D.E2y(4)-y'''-2y''+y'=0

Q: Find the general solution of 9y ′′ (t) + 12y ′ (t) + 32y (t) = t + et

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Q: Give the general solution of (D5 - 3Dª + 8D² – D – 5)y = 0

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Q: Find the solution of the D.E. below: 2(2x² + y*)«x – xycdy = 0 ... x* = c (4x²+y²) x* = c(x?+ 4y?) B…

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Q: Obtain the general solution. (D4 – D³ – 3D2 + D+2)y=0 O y= Ce* + C2e2x+ e¬*(C3+ Cax) O y= Ce-*+…

A: Solution is given as below:

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

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Q: Find the general solution of (D3 – 2D2 + D)y = x

A: (D3-2D2+D)y=xlet D3-2D2+D =0D(D2-2D+1)=0D(D-1)2=0 D=0 or D=1,1Therefore C.F.=C1+C2ex+xC3exnow we…

Q: Solve the second-order equation xy" + 2y' 8x? by making the substitution u -y'.

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Q: The solution of y = 5y + e 2"y2, y(0) = 2 satisfies:

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Q: -(D² – 25) y = x e* . Using method of undetermined coefficients, what is y Consider A ' = Ax e* + B…

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Q: 19. Find the particular solution of y" + 4y' + 5y = 2e* a. y =e* b.y =e* c. y = -e* d. y =e* 5

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Q: Solve for the solution of this D.E. y''' + 2y'' - 5y'-6y=0 Which has values of y=3, y'=6. y''=12…

A: Now , we have a homogenous differential equation . y'''+2y''-5y'-6y=0y(0)=3y'(0)=6y''(0)=12 We find…

Q: Q4\ Solve by Gaussian elimination x - 4y= 2z = 21 2x+y + 2z = = 3 3x +2y-z = -2

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Q: Use the method of undetermined coefficients to find the general solution y'' +3y' +2y =e-t +t2 +2t

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Q: I. Obtain the general solution of the following: a) (D2 + 3D + 2)y = 1 + 3x + x2 b.) (D2 − 6D +…

A: Use rules of differential equations

Q: Solve the given DE. (D³ + D² + D+ 1) y = 0 ; y (0) = 2, y' (0) = 2, y" (0) = -4

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Q: 19. Find the particular solution of y" + 4y' + 5y = 2e* a. y ==e* b. y = c. y = -e* d. y = e* 5 O A…

A: To find out the particular solution.

Q: The solution to the equation is ged (D²-D-6)y(x) = xe %3D 1 1 -xe" (5x-2) - y,(x) 50 1 د. غير ذلك…

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Q: 2. Verify that e 2 is a solution of the equation y" -3y'+2y=0.

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Q: The solution of the IVP y"-3y'-4y 0, y(0)30, y'(0) =5 is: Select one: a. y= - e 4t + e b. C. y = e4t…

A: Heew we find the solution of the IVP y''-3y'-4y=0, y0=0, y'(0)=5

Q: (b) Solve y" + e*yf + (1 + x²)y = 0, %3D x = 0, if y(0) = 1; y'(0) = 0. %3D

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Q: Solve for the solution of: (D3 + D)2y = 0

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Q: 9. Find the general solution of (D² – 2D+ 1)y= 6e*. A) y= (c, +c,x)e* + 3e™* B) y= (c, +c,x+ 3x² )e*…

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Q: 4. Obtain the general solution (D + D - 9D - Dy = 6e - X 3x + 3xe

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Q: (D² – 3D + 2)y = e2×(1 + e2x)¯ -

A: Given: D2-3D+2y=e2x(1+e2x)-1 Formula used:y=yh+yp

Q: Find the solution to the Bernoulli Equation. 2x³y = y(y? +3x?)

A: The solution is given as

Q: Find the general solution of y'' - 2y' - 8y = 24(x2+1)e4x by using VARIATION OF PARAMETERS

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Q: Obtain the general solution of the following: A. (D2 − 1)y = ex + 1 B. (D2 + 1)y = sec3x

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Q: Find the particular solution. (D^2 − 2D − 3)y = 0; when x = 0, y = 0, y′ = −4

A: From the given differential equation; D2-2D-3y=0 The auxiliary equation is: m2-2m-3=0 Now solve;…

Q: (D² – 3D + 2)y = e2*(1+e2x)

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Q: Obtain the general solution unless otherwise instructed . (D² − 3D + 2)y = e²x(1 + e²x) −¹ Yc = Ур =…

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Q: The particular solution (yp) of the equation y" - 3y + 2y = 5 e* is yp = -5xe*

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Q: Find the general solution of the following: 1. (D² – D – 2)y = 0 2. (D² + 3D)y = 0 3. (D² – 5D) + 4y…

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

Q: Solve the second order equation (d2y/dx2) = -my  with the boundary conditions y(0) = y(L) = 0, x⋲[0,…

A: Given the second order equation is d2ydx2=-my

Q: Solve the Bernoulli equation   y'-2.8y=-0.28y^2

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Q: 17 c. Find the general solution of the D.E. 2 y" +4y'-8y = 8×-4e²* +4

A: We solve given DE by using method of undetermined coefficient.

Q: g'ay-3y=(2tが)et

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Q: c) give a particular solution for y" – 2y' + y = 3e* + 1+x

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Q: Show that y = c1ex + c2e-x + c e + 3 is a solution of y ||| -2y | | - and | + 2y = 6 (justify).

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Q: Find the general solution of: x² = y² QY_ dr

A: We have to find general solution of given differential equation.

Q: 2) Find the general solution. y" + 3y" – 4y' – 12y = 0 d°x d*x d³x 12 ds d²x ds ds²

A: Here we calculate roots of auxiliary equation.

Q: 'ind the general solution of d³y 6. dr3 dy - 8y = 21e2 dr dr2

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Q: c) Using the results in a) and b), give a particular solution for y" – 2y' + y = 3e* + 1+x2

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Q: Find the general and the particular solution: d²u du = 4(1 + 3v)²; u = -1,and = -2 when v = -1 dv²…

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