2. Find the differential equation having the solution as the equation representing all lines with slope and y-intercepts equal.

Q: Show that the function y = f(x) is a solution of the differential equation.

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Q: 4. What is the differential equation of the given functions? • y = Ce-* + Cze-2x + x y = Ce2* +…

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Q: Qs: Solve the fallow ing differential equations b) (x+j) dx - Xdy-

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Q: Solve the Differential Equation (D² + a²)y = Tanax by the method of Variation of Parameters.

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Q: y + 3xy' – 2(y')³ = 0

A: Product rule of differentiation: (fg)'=fg'+gf' Chain rule of differentiation:…

Q: What is the differential equation of the family of circles with their centers on the y – axis and…

A: The given problem is to find the differential equation of the family of circles with centres on…

Q: Find the differential equation whose solution is given by: y^2=4ax

A: To find the differential equation for y2=4ax differentiating this equation with respect to x.

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

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

Q: Eliminate the arbitrary constants: y= x+ Ce2x + C2e¬x 1.

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Q: Find the general solution of the differential equation. Use C, C1, C2,⋅ ⋅ ⋅to denote arbitrary…

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Q: 5. Find the differential equation of the family of straight lines with slope 1. с. у -130 d. y' +1=0…

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Q: Obtain the solution of the differential equation y′ = (x + y)^2

A: Given differential equation is: dydx=(x+y)2                       (1) Let us assume (x+y)=t…

Q: 3. Find the complete solution of the differential equation (4x + xy2) – (y – x?y)y' = 0 using…

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Q: Find a differential equation whose general solution is y = c₁e³t+c₂e-2t 2 = 0

A: We need to determine a differential equation corresponding to the general solution: y=c1e5t+c2e-2t.

Q: Find the general solution of the differential equation. Use C, C1, C2,⋅ ⋅ ⋅to denote arbitrary…

A: y''(t)=60t4-4+12t-3 We need to find the general solution of the given differential equation using C,…

Q: 3. Determine the solution of the differential equation +-y x3 given that y (1) A ax +R

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Q: Find a differential equation whose general solution is 8t -6t y = cje + c2e = 0

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Q: Find a differential equation whose general solution is y = cjet + cze-". = 0

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Q: a. y = C,e=x + Cze-2x + x

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Q: What is the differential equation of the solution y = Cje³* + C2e-5x + Cze* Differential equation:…

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Q: form the differential equation corresponding to (y-b)2=4(x-a)

A: (y-b)2 = 4(x-a)

Q: Find the particular solution to the differential equation when y(0)=3 and (2)=1

A: Given differential equation isy''=y'2x-y'x2-1 The conditions are y(0)=3,  y'(2)=1

Q: 5. Find the solution of the differential equation using Variation of Parameters. у" - Зу" + Зу 3 E

A: Given y'''-3y''+3y'=exx

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

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

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Q: find the degree of the differential equation y''-12cosec y= 0   3 1 4 or 2

A: The order of the differential equation is 2.

Q: Solve the differential equation by variation of parameters. y" + 2y + y = e-t In(t). -t 2e t²ln t…

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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: What are the order and degree of the differential equation representing the family of parabolas y2 =…

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Q: solve the equation using differential equation linear in x and y: (2x-3y-5)dx + (3x-y-2)dy = 0;…

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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: y = cje* + cze²r y" -y – 2y = 0 O 2y " -y' – y = 0

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Q: (a) The order of this differential equation is (b) Is the equation linear?

A: Given: d2ydt2+sin(t+y)=sint To find: (a) The order of this differential equation  (b) whether the…

Q: Match the differential equation with its solution. y' - 4x'y = x3 %3D

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Q: Solve the differential equation y Pemer 6a y5 subject to the condition that y 3 when = 3.

A: Here we have to solve the given differential equation

Q: A solution for the differential equation is y = Pe-3x/2 + Qe–x/2, %3D

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Q: Use the method of variation of parameters to find & particular solution of y" – 2y + y = and write…

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

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Q: y = C1e2" sen(x)+ C2e²" cos(x) +x² + C3x + C4.

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

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Q: Find the general solution of the differential equation. Use C, C1, C2,⋅ ⋅ ⋅to denote arbitrary…

A: the given differential equation is: y'(t)=12t5-20t4+2-6t-2 we have to find the general solution of…

Q: Find the differential equation whose solution is given by y^2=4ax

A: topic - differential equations

Q: Use inspection to find four solutions to the differential equation: (y')^2+y^2=1

A: The given differential equation is

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: 5. Find the solution of the differential equation using Variation of Parameters. y"' – 3y" + 3y' =

A: We will use the method of variation of parameters to solve this question. First, we find the three…

Q: b. y = C, + Cze3*

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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.