4y? - 7y - 12 dy y(y + 2)(y - 3)

Q: b) sy- 7y-12 dy y(y+2)(y-3) 4y² – 7y-12 dy

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

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Q: (y®+ 4y³-Ay) dy y2+10 6. ,3.

A: LetI=∫y5+4y3-4yy2+10dyI=∫y5y2+10+4y3y2+10+-4yy2+10dyI=∫y5y2+10dy+∫4y3y2+10dy-∫4yy2+10dyTake constant…

Q: (D3 + 4D² + 9D + 10)y = -24e* %3D

A: Let's find.

Q: D'y- 4. (4D - 4D³ - 23D2 + 12D +36)y = 0 5. (D° + 3D² + 3D + 2)y = 0 Dy +y = 0

A: The given differential equation is: (4D4-4D3-23D2+12D+36)y=0 The auxiliary equation is:…

Q: 4. (D² +D-1)² y =0 ,when x= y = 0, y' = y" =1, y" = -1

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Q: y'' – y" + 4y'- 4y = 10e-t, y(0) = 5, y'(0) = -2, y"(0) = 0 %3D %3D

A: Given differential equation is y'''−y''+4y'−4y=10e−t, y0=5,y'0=−2 and y''0=0 Take Laplace transform…

Q: (D3 - 3D - 2)y =0; when x =0, y=0, y' = 9, y” = 0.

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Q: 3x2 +- 8(y + 1) = 0 dy y+1

A: Comparing the given equation with the equation Mdx+Ndy=0, we have M=3x2 and N=x3y+1-8y+1 Now we…

Q: (c) 6e2z-y (d) x+y ; y(1) = 2 (e) y' +y = e² y(0) = 1 %3D

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Q: y² – 2x ry? dy = 0; y(-1)

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Q: d² (2у) (2y). (4y) -(16у) %0 dy? dy

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Q: 4y -7y-12 dy y - y -6y 3 2

A: The integral is ∫124y2-7y-12y3-y2-6y.

Q: cx-dy=c^2+d^2 x+y=2c What is x?

A: Please refer the attached image for complete solution.

Q: y" – 2y' + y = x², y(0) = 3, y'(0) = 2. -

A: y′′ −2y′ +y=x2 Second order linear non−homogeneous differential equation with constant…

Q: 2 y (4- y²)³ dy

A: The objective of the question is evaluate the definite integral.

Q: 1. If y? = 10x , then dx2 d²y 5x А. 2ху 2y 5ху С. D. 2x 2 B.

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Q: (D³ – D)y = 4e * + 3e2* %3D y" = (-Axe* + 3Ae*) + 8BE2* %3D

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Q: (D²-3D-2)y = 0 Find y when x = In 2 when x=0, y'= 9, Y=0, y=0 4.

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Q: (y²-9)y' + e =t, y(2) = 2

A: y(t)2 -9y'(t) + e-y(t) = t2 , y(2) = 2                     first order nonlinear…

Q: x = u3 + 7 ; y= 6u? – 1 d²y ---> dx2

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

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

Q: y" - 2y' + y = 4e-t + 2et, where y(0) = -1, y'(0) = 2

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Q: Maanze; Z こ5x +y Subject to Lラトーメ 5x +3y 575 X20,4? 0

A: Maximize Z=5x+y Subject to, x-y≤75x+3y≤75x≥0, y≥0 The graph is,

Q: +(ux+y-3) dy=D0 Q=Ap(5-人+以り)+ Xp[^ーメ2)

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Q: y" - 2y' + y = 2xe2* + 6e*, a) y(0) = 1, y'(0) = 0. %3D %3D

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Q: 2. y³ = 2a°x³ , find y". 3. 4x° = 3y*-x³y? , find y" %3D

A: Note: Since you have posted multiple questions, we will solve the first question for you. if you…

Q: y" + 3y' + 2y = 2x – 1, y(0) = 0, y' (0) = 0. %3D -

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

Q: y"+ 7y + 10y = -5te. Yp e^(5t)(-1/14t-19/140) %3D

A: We have solve pi

Q: dy 2. a-y = ry, y(2) = 0 dr

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Q: xla? - y² - x) dx - y(x² - y²) dy = 0 2 XX 2

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Q: 2 V4-x2 e*²+y* dydx =? -2 0

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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: Y" - 4 Y' = 6e3t - 3et, Y(0) = + 1, Y'(0) = -1 %3D

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Q: y - 3y = 8(t - 2), y(0) = 0 %3D

A: We have to solve the given ode using laplace transform.

Q: y3 + y2 + 5y + 4 -dy y2 – y + 3 8.

A: ∫y3+y2+5y+4y2-y+3dy

Q: c) y'=X-y+1 x-y+2' with y(1) = 2.

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Q: [y(8y² -5)dy 4y* -5y? +5 1.

A: We can find the answer as below

Q: (3x²y + 2ry +y) de + (x² + y³) dy = 0

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Q: y - dy (y + 4)(2y – 1)

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

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Q: -2 2 /y + 2 dy + √ ² [√y+2_y] dy

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Q: 4. (D² +D-1)²y = 0 ,when x= y = 0 , y' = y" = 1, y" = -1

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Q: 3. y² +4y-4 √√y dy

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Q: 1- y" – 3y' + 2y = 4e2t y(0) = -3 y'(0) = 3 %3D

A: This is a problem related to the differential equation. By Laplace transform method first of all we…

Q: 2. y²dx + (x² − xy - y²)dy = 0 [Answer: (x - y)y² = c(x + y)]

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Q: (3ry- 1) dr + (x³ + 6y – y?) dy = 0 y(0) = 3

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Q: 9. ydx - 4xdy = y'dy; y(4) = 1 Ans: -y²=

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Q: 1 y dy Sza 3 (a²-y²)²

A: