6. (D - 4D2 + 7D)y = 0 (D3

Q: (D4 + 3D3 – 6D² – 28D – 24)y = 0 (D3 + 3D2 + 3D + 2)y = 0 -

A: 2) (D3+3D2+3D+2)y=0 The auxiliary equation is…

Q: Vy - y 3 b) dy 2 y²

A:

Q: 3. (D3-2D2+D-2) y=0 4. (4D3+28D²+61D+37) y=0

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Q: d²y dx2 -y = 10sin²x

A:

Q: 17. y"-5y6y=t² + 7, y(0) = 1, y'(0) = 0

A: For an initial value problem with boundary conditions available, we have to convert the given…

Q: d²y Find if 2x'-3y=7 dx²

A: Given that       2x3 - 3y2 = 7 Here we have to find     d2y/dx2

Q: Find dy 2x-3y=8 2 if dx2

A:

Q: dy Find if y 3e2 3z 一山 %3D O -9e 2

A: Using chain rule of differentiation.

Q: Find d2y/dx2 if 2x3-3y2=8

A:

Q: calculate d2y/dx2 when y=.4x-.3

A: Given function is y=4x-3. Power rule of differentiation states that: ddxxn=nxn-1 Differentiating the…

Q: 1. (D³ - 3D²D + 3)y = 0

A: To Solve: (D3-3D2-D+3)y=0.

Q: 32 8y%dy y-15 2.

A: The given integral is,

Q: Non Homogeneous: (D2 − 7D + 6)y = 3x2 − 2x + 5

A: Here we have to solve the non-homogeneous differential equations     (D2-7D+6)y = 3x2 - 2x +5 .

Q: - / 4(1-)esc2(1– y)dy

A:

Q: 4. (D² – D – 6)y = 0; when x = 0, y = 3, y' = -1 %3D

A: Use this auxiliary equation and complementary function

Q: y = x(2x+1), y" y = (4x − 3)¹/²2, d³ y dx³

A: Topic:- derivatives  Note :- as per our guideline if more than one question uploaded than only first…

Q: 2 2X-) dy tf2 るメー。 2. Y+2

A: We have to solve the given differential equation.

Q: d*y + 2 dx3 d³y , d²y 8. dx4 = 0 dx2

A:

Q: (D³ – D)y = –2(1+x) + 4e* – 6e¬* + 96e3x -

A: Given- D3-Dy=-21+x+4ex-6e-x+96e3x To Solve- The above differential equation.

Q: 4. (D2 – 5D + 6)y = 15sinx – 15cosx -

A:

Q: Find dx2 d²y if x = 3cos4t and y = 6sin4t. %D

A: Eliminate the variable t and form a equation in x and y only than take two times derivative.

Q: · (D² + 3D + 2)y = xsin 2x

A:

Q: 10. (D² – 2D – 3)y = 0 when x = 0, y = 0, y' = -4

A: To find the solution of the given differential equation .

Q: Find d² y dx² for x³ + y³ = 2 43

A:

Q: (D5-11D4+19D³ + 115D² - 200D - 500)y = 0 Ans: y = C₂e-2x + C₂xe-2x + C₂e³x + ₂x³x + C5x²e³x

A:

Q: d3y find 3 5) If y = 4x + z %3D dx3

A: Given that: y=4x3+3x2

Q: - y² dy 3y 50.

A: Simplify the expression and integrate it.

Q: 9. (D²+4D+5)y-35ex:y(0) --3, y'(0) - 1

A:

Q: 3) S dz z3-z2-6z

A: In the question it is asked to calculate the integral of the following function given:

Q: d²y x-9 Find for y dx2 = (3x² –2x+5)

A:

Q: d²y + 4y = 8x² ,y(0) = -3,y'(0) = 0 dx2

A: We have to solve the differential equation using initial conditions.

Q: (D³ - 4D²D'+ 5DD² – 2D ) z = e'+2* + Vy+x. |

A:

Q: Find d2y/dx2.  y = 2/(2 + x2)

A: Given: y=22+x2

Q: 3. (Dª + 3D³ – 6D² – 28D – 24)y = 0 -

A:

Q: Find d2y/dx2 if 2x3 - 3y2 = 8

A: Given:

Q: + 12D + 36)y = 0 5. (D³ + 3D² + 3D + 6 (D3 AD3

A:

Q: (D3 – 3D2 + 9D + 13)y = 0 sle plel Ja

A: The given differential equation is ;                    D3-3D2+9D+13y = 0 We have to find the…

Q: 1. (4D5 - 8D4 – 17D3 + 12D² +9D)y = 0 2. (D® – D°)y = 0 3. (D3-D2 - 4D – 2) y = 0

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Q: (D3 – 2D2 – D + 2)y = 10sin2x – 5cosx - -

A:

Q: 5. (D5-11D4+19D³ + 115D² - 200D - 500)y = 0 Ans: y = C₂e-2x + C₂xe-2x + C₂e³x + C₂xe³x + С5x²e³x

A: To Solve: Solution of ODE

Q: 5. (D2 – 5D + 6)y = 18x2 + 12e2* (Assume yp = Ax² + Bx + C + Ee2x)

A:

Q: If y=3xe , then what is d²y. 3x dx 2

A: Let's find.

Q: DY =-3(2) +8 ay=-463) +28

A: 1) given   Y = -3(2) + 8 here by using BODMAS rule we can can solve the equation B => Brackets -…

Q: (D² – 8D + 16)y = 4e¬v2t, y(0) = -1, y'(0) = 3;

A:

Q: (D² + 6D + 7)(D3 – 5D² + 6D)y = %3D

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Q: (D - 2D + 4)y = 0 ; y= - 2, Dy = 8, D²y = 0, when x = 0.

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Q: d*y d³y - 4· dx3 +7 d²y 14 dx4 dx2

A:

Q: + Vs + es +- ds n = 3 From left endpoint s² + 1

A: