Find the differentials of each of the following. 1. у%3D 5x4 —Зх3 +х—6 2. y=- v+ 3. y= x²(1– x²)=

Q: 1. y = c1e-2x + cze²x + cze2x 2. y = c1e* + cze3x

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Q: 5x y = C, + C2e4x 4

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Q: For what value of x will the curve y = x3 – 3x2 + 4 be concave upward?

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Q: The pressure, volume, and temperature of a mole of an ideal gas are related by the equation PV =…

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Q: Determine the differential coefficient of y= V3x2 +4x -1

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Q: Find a differential equation whose general solution is y = c₁e³t+c₂e-3t 5t = 0

A: The general solution,y=c1e5t+c2e-3t

Q: solve the differential equatior y"-8y'+16y=O

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Q: Determine whether y = 2x is a solution of the differential equation y'= 6x², a. 6x2- and by'= 6r?…

A: Just take derivative of y and substitute in given differential equation and see if it satisfies the…

Q: Find the solution of the Linear Homogenous Differential Equation with Constant Cofficients. (D³ +…

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Q: 3/xyy' = 5

A: We have to solve the differential equation  3xyy' = 5.

Q: Please help me with this differential equation and identify P(x), Q(x) and v(x).

A: The general form of first order  linear differential equation is shown on board

Q: What will be the order of the differential equation if its solution is y=Acos7x-Bsin7x a. None of…

A: Homogeneous Linear Differential Equation with Constant Coefficients: A homogeneous linear…

Q: Find the differential equation whose general solution is y = C1x + C2ex. %3D

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Q: y' – 4y = –1et and y(0) = -2.

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Q: 2. (x +1)y'+y = x² – 1 %3D -

A: Topic = Differential equation

Q: Solve the differential equation 2xyy' = 1 + y". If y = 3 when x = 2, determine y when x = 1.

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Q: Please help me solve this differential equation and identify P(x), Q(x) and v(x).

A: First we rearrange the equation and find P(x) and Q(x)

Q: 6. y = c,eaxcosbx + Czeaxsinbx and a and b are

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Q: Find a differential equation whose general solution is y = c₁est + c₂e-2¹. 5t = 0

A: I have given the answer in the next step. Hope you understand that

Q: For an ideal gas, the pressure is related to temperature and volume by the formula 8.31T . If your…

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Q: Find the differential equation whose general solution is y=c1e4t+c2e-5t

A: Find the differential equation of given solution.

Q: Find the differential equation having the solution as: a. y = C,e¬x + C2e¬2x + x b. y = C, + C2e³x

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Q: Find a differential equation whose general solution is y = c₁et + c₂e-4t . = 0

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Q: 3) For an ideal gas, the pressure is related to temperature and volume by the formula 8.31T V . If…

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Q: Solve the differential equation by variation of parameters. y" + 3y + 2y = 8 1

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Q: y(4) 4х + 2хе %3D

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Q: Find a differential equation whose general solution is 9t y = c₁e⁹t + c₂e-²t = 0

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Q: What is the degree of the differential equation dy = 5a4 – dr3 6x2 ? |

A: Clearly the exponent of (dy/dx) is 3.

Q: What is the differential equation of 2y'=3y+1 when y(1)=0

A: Consider the provided D.E 2y'=3y+1  when y1=0 We need to find the solution of the given D.E, Since,…

Q: What is the solution of the differential equation of (2x° + ry? + 2y +3) dr + (x²y + 2x) dy = 0 ?

A: We have given differential equation,   Differential equation is of the form,     Mdx +Ndy=0 Firstly…

Q: Find a differential equation whose general solution is 7t y = c₁e¹t + c₂e-2t. y" - 5 y' - 14 y = 0 ✓

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Q: Find a differential equation whose general solution is 9t = C₁e⁹t + c₂e-5t. y = = 0

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Q: Find the differential equation such that y(x) = c₁(x-4) 8 +c₂ln(x-4) (x-4) 8

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Q: 3. Write the the differential equation by separating the variables. dy = 7x-2 dx

A: Given,          dydx=7x-2

Q: Write down the solution of the differential equation: y +4y +3y x2 -5x +4 if y(0) = 0 and y (0) =1

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Q: In tracking the propagation of a disease, a population can be divided into 3 groups: the portion…

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Q: 4) For an ideal gas, the pressure is related to temperature and volume by the formula 8.317 P = If…

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Q: ry? V1+ x²

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Q: Solve the differential equation as follows: (3 + 5x?y³ + 4xy* + 3y³)dx + xy²(3 + 4xy + 3x)dy = 0

A: To solve the differential equation as follows: 3+5x2y3+4xy4+3y3dx+xy2(3+4xy+3x)dy=0

Q: s, p°+ 3 xp²- yp²-3xyp = 0 find the differential equation

A: Given: p3+3p2−y3p2−3y3p=0 The standard notation for p is p=dydx.

Q: Find a differential equation whose general solution is y = c₁e5t + c₂e-²t. = 0

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Q: Find a differential equation whose general solution is 7t y = c₁e²t + c₂e-5t = 0

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Q: Write down the solution of the differential equation: y+4y +3y 0 if y(0) - 2 and y (0) =3

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Q: Find a differential equation whose general solution is -4t y = cjet + cze¬4.

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Q: Q3: if y'-f(y/x) where v-y/x Find a solution to the differential equation 2xyy'-y2+x2 =0 ?

A: Given

Q: The differential equation formed from y = Ae3* + Be7ª is: y"-10y'+35Y3D0 y"+12y'+35y%3D0…

A: we have to form the differential equation from the given equation. I have explained in details…

Q: Find a differential equation whose general solution is 6t y = c₁et + c₂e -3t = 0

A: We find a differential equation whose general solution is y=c1e6t+c2e-3t.

Q: (D² – 2D + 5) y = 25x² + 12

A: Given: D2-2D+5y=25x2+12 So,  The auxiliary equation is: m2-2m+5=0 Now solve; m2-2m+5=0m1,…