(f) The equation y - y = a + x² + 6 has no solution over Z[V10]. (g) The equation y7 - y = x³ – 7x + 9

Q: Use the method of reduction of order to find another solution of y"−4y'+4y=0 if y₁=e²x is a solution…

A: The given equation is;  y''-4y'+4y=0 and y1=e2x

Q: How to solve this equation y'''+2y''+4y'+8y=(5e^3t) + 1 using Variation of Parameters with wronskian…

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Q: Find the particular solution that satisfies the initial condition. x3y'+2y=e1/x^2, y(1)=e

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Q: Find the general solution of: y(x°+x*)dx - x(x³+ y-)dy = 0

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Q: Find the formulation of a particular solution of y" + 3y' +2y = 3+t2 – te-2t cost without…

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Q: Find the solution by using Solution of 2nd order D-Es 2 X ý XỨ ty - xy + y = Lnx -

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Q: Obtain the general solution. xy3dx+ex^2dy=0

A: The given differential equation is xy3dx+ex2dy=0. We have to obtain a general solution.

Q: ) Obtain the general solution of y" + 2y + y = e² In r

A: In this question, the concept of the differential equation is applied. Differential Equation A…

Q: find general solution. dr/dt= -2tr,         r(0)=ro

A:

Q: Find the general solution of y’ + (1/3)y = exy4

A: We have to find the general solution of the differential equation y'+13y=exy4 .

Q: Find the general Solution of DES: x yy'= x +3y

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Q: find the general solution of (y^3 + yz^2 -z)dy + (z^3 + y^2 z - y) dz = 0

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Q: Find the general solution to t²y" +2ty' - 2y = 0 given that y₁ (t) = t is a solution.

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Q: Find the general solution using variation of parameters. y" – 4y + 4y = (x + 1)e²"

A: Given differential equation is, y"-4y'+4y=x+1e2x The auxiliary equation is, m2-4m+4=0m-22=0m=2,2…

Q: yV + 2y" + y" = re=*

A:

Q: dy Solve of y = e2-3+18 In(e2²-30+18 da A. y' e2z²-32+18 (8x3 – 18z² + 85x – 57) B. y' e2a2-3a+18…

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Q: Find general solution of y" – 2y' + y = , By Variation of t2+1' parameter method.

A:

Q: . Find the general solution of (³ + 2y*)y' = 3ya² in implicit form f(x,y) = c. When y(0) = 1, what…

A: We have given differential equation  x3+2y4y'=3yx2…

Q: Find the general solution by using reduction of order method to (x2 + 1)y" – 2xy' + 2y = 0 given…

A:

Q: (a) Solve y" + xy + (2r – 1)y = 0, %3D near z = -1, if y(-1) = 2; y'(-1) = -2.

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Q: Find a general solution of y"- iy'+6y= 0.

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Q: Find the general solution using variation of parameters. - 4y + 4y = (x + 1)e²-

A: To solve the following problem

Q: 1. Find the general solution using variation of parameters. y" – 4y + 4y = (x +1)e²r

A: Solve by using variation of parameters.

Q: Find general solution to Cauchy-Euler equation: (t^2)y''-2ty'-3y=t^2

A:

Q: 8. What is the particular solution of 2xyy' =1+y², when x = 2, y = 3 ? а. у%3D5x -1 C. y =V5x + 2 b.…

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Q: Show that y = - In x + 3x - 5 is a solution of y" -=0. Use y = - Inx+3x – 5 to find y' and y". y' =O

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Q: Find the general solution of ди ди (y – z) + (x – z) ди + (2y – 2x) ду - az

A: The differential equation is given as (y-z)∂u∂x + (x-z)∂u∂y  + (2y-2x)∂u∂z = 0 We will solve it by…

Q: 3. Find the general solution of y" – 3y' + 2y = e" using the method of variation of parameters.

A:

Q: x+3y+z=90     7y+2z=56 Using the echelon method

A: observe that the number of variables is great than the number of equations. So, one of the variables…

Q: what is the general solution of y (1 + 3x ) y - v ? Oy = 4 + 3x + Ce %3D = 4 +3z + Ce" 4 + 3x + Ce…

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Q: Obtain the general solution valid near the origin: 2y'+9ху'-36у 30

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Q: Obtain the general solution using variation of parameters. (D^2 − 1)y = e^x + 1

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Q: b) Give a particular solution for y" – 2y' + y = et - 1+x2

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Q: 2. Find the general solution of y' = eY(4x – 2). %3D |

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Q: Find the solution of y-x =0 using separable variable method. dx

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Q: (b) Find the general solution of: əz = yx² - xy Əx Given z = y when x = 1, determine the particular…

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Q: 2. Obtain the particular solution. y"-y'-6y=0; when x=0, y=2,y'=1

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Q: Find the general solution of (x³ + 2y4)y' = 3yx² in implicit form f(x, y) = c. When y(0) = 1, what…

A: We have to solve the differential equation

Q: Find the general solution of the equation 4y'' + 4y' + y = e-t/2

A:

Q: Use variation of parameters d²y +pdty+94=Fx) plem) to find a particular solution to y" – 2y - 15y =…

A:

Q: determine the general solution of y''-y=0 given y1(x)=e-2x using reduction of orders

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Q: Find general Solution of y + +y+ 4y = Ct1)e Using method of vanafion.

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Q: X-2y+3z=11 4x+2y-3z=4 3x+3y-z=4 Solve by  Gaussian elimination

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Q: Find the Solution to Homogeneous LinearEquation: (D3-3D2-3D+1)y=0

A: Given equation is D3-3D2-3D+1y=0 find the solution of the given equation.

Q: Solve for the general solution. d³x dx -7. - + 6x = 0 dt3 dt

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Q: OBTAIN THE GENERAL SOLUTION (x - 1) dx - (3x - 2y - 5) dy = 0

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.