Find the general solution of the DEs 1- f"(x)= y"(x)=12x +6x-8

Q: 24- ex +12x²-6,yc0)=2, yo)=3

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Q: Find the general solution valid near x=0 (x2 + 4) y" + 2xy' -12y = 0

A: We have to solve given problem:

Q: Find the general solution of x(x + 3)dy = 2dy + √(9- y²)(12x + 9 + 4x²) dx.

A: We will separate variables and then will integrate it to find general solution of given differential…

Q: 11. Find the particular solution of 2ydx = 3xdy, when x -2, y = 1

A: Given : Differential equation :  2ydx = 3xdy And x = -2, y = 1   To find : Particular solution of…

Q: 3. Solve 2x²y" + xy' − 3y = 0 with the initial condition y(1) = 1 y′(1) = 4

A: This is a Cauchy Euler equation. The equation is solved by a substitution.

Q: Solve the initial value problem : f'(x)= x" – 4x³ + 12x + 18 and f(0) = 6.

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

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Q: Solve the initial value problem: f'(x)=5x^28 -6x^5+12x+12and f(0) = 6

A: We have to solve the initial value problem  f'(x) = 5x28 - 6x5 + 12x + 12  f(0)= 6  Integrate both…

Q: 2. Find the general solution of the first-order equation dy _ y² – 2ry dr

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Q: The general solution to y'' - xy' + y = 0 is given by:

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Q: Give a particular solution for y"– 2y' + y = ; ex 1+x2

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Q: In(ax) f(x) has a stationary point at Find a and b. bx 2' 3e,

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Q: x" – 2x' + 4x = d(t – 1) x(0) = x'(0) = 0 - -

A: For solving this question we use the table of Laplace transform and properties of Laplace transform…

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

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Q: Solve the initial value problem: (x + 2) y' = xy + 2y - 3x - 6 When x=0, y=1

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Q: Find f(x) by solving the initial-value problem: f' (x) = 3ex + 2x2;  f(0) = 5

A: The derivative of the function, fx: f'x=3ex+2x2; f0=5.

Q: Find the general solution to y" – xy' = 0. -

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Q: 13.Obtain the general solution of y²dx+x(x +y)dy = 0

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Q: What is the general solution of xydx−(x2+3y2)dy=0

A: Topic :- Differential equation

Q: Find f(x) by solving the initial-value problem: f'(x) = 3e2 +2x2; f(0) = 5

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Q: Find the general solution to xy′′−3y′=0.

A: We have to find the general solution of the given differential equation.

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

A: Given that a differential equations - y" -2y' +y = ex/1+x2.   We know that integration of 1/(a2 +x2)…

Q: Find the general solution of (x^2+x)dy=3dx

A: Given difeerential equation, (x2+x)dy=3dx

Q: Solve the initial value problem: f'(x)=x^15 -7x^3 +12x^2+14 and f(0) = 7

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Q: der the problem maxx + 2y subject to x² + y² ≤ 1 and x + y 20

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Q: 12. Find the general solution of x²dx + y(x – 1)dy = 0

A: This is a variable seperable DE.

Q: H4. Use the method of variation of parameters to find the general solution of dy -X- - 3y= 4x³. dr2

A: Please find attachment for the details solution

Q: If the function f(t) is a solution of the initial-value problemy′ = (2t + 5)y, y(0) = 3, find f (0)…

A: To Determine: if the function f(t) is a solution of the initial value problem. find f(0) and f'(0).…

Q: Give a particular solution for y" – 2y' + y = ex 1+x2

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Q: 2. Solve y' = 2x(x² – y), with initial condition y(0) = 1. -

A: This is first order linear differential equation

Q: What is the general solution of xy^2dx+x^2ydy=0

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Q: Find the general solution to / + (xy)² = y²e%* .

A: since you have posted multiple question in this question which are not interlinked so i have solved…

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: ) Give a particular solution for y" – 2y' + y = 1+x² *

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Q: 4. Solve the IVP y' = 2x-3y +e¯* y'= 2x- 3 y +e * with y(0) = 1 y(0)= 1

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Q: 3. Obtain the general solution of: (x – y)(4x + y) dx + x(5x – y) dy = 0

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Q: 8. Find the particular solution of x²y"+ xy' = 1; y = 0 and y' = 1/2, when x = 1.

A: eular method

Q: Solve y' = 6x, x' = x + y with initial conditions x(0) = 1, y(0) = -2.

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Q: Solve this initial value problem: xy-y=xlnx )=2

A: problem is related to first order differential equation

Q: The general solution of 5uxx – 6uxy +uyy = 0 -

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Q: Solve the initial value problem y'=x^2-4x+3-6e^x, y(0)=8

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Q: Find the particular solution of: y' – 4y = x²e* that satisfies y(0) = 2.

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Q: Find general solution of the DE 4y′′′ + 4y′′ + y′ = 0

A: The given equation is 4y'''+4y''+y'=0. The characteristic equation of the given differential…

Q: Find a general solution to (x+1)x²y" + xy - (r+1)³y=0.

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Q: Find the general solution to 3 1 0 0 3 1X. -X= dt 0 2

A: We first find eigen values, then corresponding eigen vector to solve the given system as in next…

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

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Q: 1 Find the general solution of x'y" +xy' -y= x+1

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

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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.