25. Which is a solution of the equation y = x -3? A. (2, 1) В. (-1, -4) C. (0, 3) D. (3, 6) 25.

Q: gent lihe equation. (4) x²-xy +y =7 P,(-1,2) (5) xe' -ye = 5 P(4,1)

A:

Q: 10. Solve IVP: 3y" + 2' + y = 2e ', y(0) = 1, 3/(0) = 0. -t

A: For given differential equation,   We have to find solution with given initial values.

Q: 3. Verify that y= 3e-2x + 4e* is a solution of the equation y" – 3y' + 2y = 0

A:

Q: Solve for X,Y and Z:  3x + y − z = 11x + 3y = z + 13x + y − 3z = 11

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Q: 4. Šolve Člairaut equation y = xy' – 2In(y' +1)

A: The given clairuat equation y=xy'-2lny'+1 s the first order nonlinear ordinary differential…

Q: Solve y'" – 4y' + 20y = – 68e*, y(0) = 0, y'(0) = 0| - y(t) :

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Q: 31. If 9x² = y(y – 3)², show that (y + 1)² ds - dy². 4y

A: We know that Given Firstly, we find dx in terms of dy

Q: 5-4y2 dy 3+2y

A: To evaluate ∫5-4y23+2ydy

Q: Find ƒx (x, y)  and ƒy( x, y) .

A: Differentiate the function f(x,y)=ln|2x2+y2| with respect to x and keeping y as constant and carry…

Q: Solve y" + y = 8(t – 7) – 8(t – 27), y(0) = 0, y' (0) = 1.

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Q: (x) + Find the general solution аху- х+у о у-xlncxЈtc 2 x² Ў= х²-хутуг у-х- х Нихте з y = x + y + y…

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Q: Solve, using the method of variation of parameters: et y" – 2y' + y =: 1+x²

A:

Q: f (x, y) = x+ 5y 2 +y = 25,

A:

Q: Determine whether y(x) = 2e-* + xe-* is a solution of y" + 2y' + y = 0. Is y(x) = 1 a solution of y"…

A:

Q: Find the number of positive integer solutions (x, y, z, w, t) to the equation 2x + 3y + 4z + 3w + 2t…

A: Find the number of positive integer solutions x,y,z,w,t to theequation 2x+3y+4z+3w+2t=20?

Q: 27) y"+2y'+ y = e", y(0) = 0, y'(0) = 0.

A:

Q: T + 4y – 6z =-1 2 2x -y+2z = -7 --x + 2y - 4z = 5 The solution is (z,Y, 2) = ):

A:

Q: 5) To find B from Mathematical equation Y = V5X + 3X +1 %3D N=Y-4Z+C? B =N X+ Y

A: Given:  Y=5X+3X+1N=Y-4Z+C2B=NX+Y To determine: The value of B from Mathematical equation.

Q: 2. -4 y= 글x + 1 y = + 6 m = m = 23 4 5 주. . t. 5. 9. b = b = SOLUTION:

A: The equation of a line is given by y=mx+c in one form. The other form of a line is given by ax+by=c.…

Q: 4. Solve eu, - uu, = 0, u(0, y) = -y %3D for small |r.

A:

Q: Solve: y''y' 6y = - 12t + 28 - y(0) = -6, y'(0) 21 y(t) =

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Q: Solve using MUC: '-8y + 16y=2(x+12) 3 y= C, e^X + C,xeAX + 8. X- 2 7 3 y=C; eX + C,xe^* + 7 X- 2 B…

A:

Q: 1. Solve ,analy hically., the fallowinng differencerequ. a. C- YCK+3) +2 y(km2) +oi45y(k+i) +0105…

A: As you require, we will solve this question on the given difference equation purely analytically.

Q: Find the points of intersection of x = 4y and y = 4x. (ans.:(0,0),(16,64))

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Q: Solve y'"+ 5y' + 4y = 0, y(0) = - 8, y'(0) = 17 y(t) = %3D

A:

Q: Solve for x, y z from X - 1 1 2 Z 3. 6 6

A: 2x-113y=2z66

Q: 6. dy 2 y (1-√y) ²

A: Given integral ∫dyy(1-y)2 The objective is to evaluate the integral.

Q: 8- By using Diret metheds solve the linear algebric Equation e- 15X + 3 y + 27 = 85 X - 2 y + 82= 5…

A: As per the company's guidelines, we are supposed to solve first question for you, kindly repost…

Q: solve 2 (pedoe tydy +2d₂) ² 2 = {(2²-x²=y²2) (seds tydy + z dz/d2} z

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Q: 3x – y + z = –1, -x + 3y – z = 7, u+ 3z = -7.

A: Given: 3x-y+z=-1 -x+3y-z=7 x-y+3z=-7

Q: 4. Y= C, ex + C2e* + X

A:

Q: solution for z(x, 0) = x², z(1,)

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Q: Solve : 2we +3ux u (x, 0) = x Solve : Sub yeck to u (x, ,0) = x+y 4.

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Q: 2) Solve for x and y. 45° 13V2

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Q: D.(1,2), where f(x, y) 14x-y in the directionof v (2,-1)

A:

Q: dr = a(p- 1)(q-), dt

A: In this question, we solve the given initial value problem dxdt=α(p-x)(q-x)withx(0)=0.

Q: (4) B/ If Ø = (x³y²z) and A = 2xz 1-3y2j+ 3xy²k Find ?у ?х the point (2, -1, 3)? at

A: Given:        ϕ=x3y2z         A=2xzi^-3y2j^+3xy2k^         ϕA=x3y2z2xzi^-3y2j^+3xy2k^…

Q: Solve y'+ 8y' + 15y = 0, y(0) = 5, y'(0) = 19 | y(t) = %3D

A:

Q: Solve y" – 4y' + 6y = 8(t – 3), y(0) = 0, y'(0) = 0. -

A: Use Laplace table.

Q: Find the Particular Solution indicated. (Homogenous Linear Equation with Constant Coeffiecients)

A: Given : Homogenous Linear Differential Equation with Constant Coefficients               D2+D-12y=0…

Q: у4у? -16у +19 dy (y-2)°

A: This indefinite integral can be solved by the substitution method.

Q: The solutions of the equation 2r + 4y = 6, x, yEZ, are O a. a= -2t, y =3+4t, teZ b. = 3+2t. y =-t,…

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Q: 4. Find the solution for the following y""+y"+ 2y = 3 y(0)= 1, y(0)=1,y)=1

A: Solution :-

Q: ·S- Find y dy Vy+2 using the substitutionu +5=√√y+2. A √y + 2 − 5 ) ( 5 √√y + 2 + y +24) + C (В…

A:

Q: d. VxVy, Q(x + 1,y/2) e. 3xVy3z, P(x,y,z)-4 > 0

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Q: (y-7) dy 4 (y+3)3

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Q: Find the general solution by Variation of Parameters. y''+y=3cscx

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Q: 5. ( : Solve the IVP: r²y" = (y)², y(1) = 1, y'(1) = 1.

A: A differential equation with an initial condition is called an initial value problem. The initial…

Q: Evaluate B: А: Vye-y° dy 3e-4z2 dz 0, 0,

A: There is a general integral that gets calculated with the help of β function. The integral is…

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.