(D² – 4D+ 7) Y = 0

Q: 2x+y 4ー dそdXdy -V4-y2

A: Triple integral is an integral of an integral with respect to three different variables. the…

Q: 2) (D² +6D+91)y= 16e-3x x² +1

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: (D^2+2D+2)y=e^-x(cscx)

A: To find any general solution of a differential equation we have to find complementary function and…

Q: Q2. (a) dy = (x + y + 3)² (b) 2xy4 = 4x² + 3y?

A: Given that a)dydx=x+y+32 b)2xydydx=4x2+3y2

Q: (Dª + 3D³ – 6D² – 28D – 24)y = 0 -

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Q: -. (D² +4D+4)y=-x*e y =-x³e

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Q: 3t y" - y' - 6y = t²e³t - 4t², y(0) = 0, y' (0) = -1

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Q: dx -7- +dd 24-y=3t73t 6t-3e

A: The given first order linear system of equation can be written as: D+2x+D−1y=3t2−3e−t…

Q: 2 2X-) dy tf2 るメー。 2. Y+2

A: We have to solve the given differential equation.

Q: d²y +y D0 dx2

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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 -

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Q: So* - y-³) dy 2.

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Q: (D² – 9D)(D² – 8D + 7)y = 0 |

A: We have to find the solutions of the given differential equations

Q: d²y Find dx2 if –10x – 6y = -6.

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Q: D² + D – 1)²y = 0 ,when x= y= 0 , y' = y''' = 1 , y" = -1

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Q: - y² dy 3y 50.

A: Simplify the expression and integrate it.

Q: (D²+4D+5)y=35e : y(0)--3, y'(0)-1

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

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Q: Find d2y/dx2.  y = 2/(2 + x2)

A: Given: y=22+x2

Q: (D³ + 7D² + 19D + 13)y 0 when x = 0, y = 0, y' = 2, y" = -12

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Q: (D² – 6D + 9)y = 0 ; x = 0; y = 0; y' = 2 %3D %3D

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Q: (d) y" – 6y" + 11y' – 6y = e2" (5 – 4x – 3a²)

A: Given  A non homogeneous differential equation in question 2. D.

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

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Q: (D² +D-1} y =0 ,when x=y=0, y'=y" = 1 , y" = -1

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Q: (D³ + 3D² + 3D + 2)y = 0

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Q: (D3−D2+4D−4)y=0 ; y(0)=2, y'(0)=7, y"(0)=-3

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Q: y = (t² – 2)². a²y 2. dx²

A: y=t2-22 and x=t2 Now, differentiate the given function with respect to t.…

Q: . (D²+1)y= 10e²x When x = 0, y = 0, y' = 0

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Q: (D² + 3D – 4)y(x) = 12e2x

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Q: d. xy' – y – 5x* – 3x² + 2x = 0 when x = 1 and y = 2 -

A: first write teh differnetia; equation in standard form and then solve.

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

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Q: d'y Calculate dx2 y = x2

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Q: y' +2y = -x8y5 will be transformed to the follo"

A: Given: - The Bernoulli's equation is, y'+3xy=-x8y5 To transformed: - The given Bernoulli's equation…

Q: Find d2y/dx2 simplify in terms of x and y x2+y2=4

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Q: (D³ + 7D² + 19D + 13)y = 0 when x = 0,y = 0,y' = 2,y" = -12 %3D %3D

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Q: The Yp of (D²+D) y=20

A: Given (D2 + D) y = 20 To find yp(x)

Q: (D² +D-1)y=0 , when x=y=0,y =y" = 1 , y" = -1

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Q: 3. (4D +4D2 + D)y = 0. 7. (4D3 - 3D+ 1)y = 0.

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Q: 6. (D³ + 2D²)y = 0; when x = 0, y = -3, y' = 0, y" = 12

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Q: (D³ + 2D*)y = 0 y(0) = -3 , y'(0) = 0 and y"(0) = 2

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Q: y" - y' - 6y=t²e³t — 4t², y(0) = 0, y' (0) = -1

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Q: (9y)° D92° E (5x - 7) 36°

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Q: (20" + 6a²)dæ + 6x²) dæ Find (2,x7

A: ∫(2x7+6x2) dx

Q: d²y Find dx2 x = t* - 8, y =t – t2 %3D

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Q: V16-x² (c) S dx 2х

A: Rewrite the given integral as shown below: ∫16-x22xdx=12·∫16-x2xdx

Q: 1. (D² + 4D + 5)y = 50x + 13 e3x

A: