2. Solve and state the largest interval over which the general solution is defined: dy (x+ 2)´ Jr = 5 – 8y – 4xy

Q: 1. Find the complete solution of ydx + (x + y²)dy = 0

A: Note: As per our company guidelines, we are supposed to answer only one question. Kindly post other…

Q: 2. Solve and state the largest interval over which the general solution is defined: dy (1+2)- ry…

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Q: xarctanydx + dy = 0 2(1+ y²)

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Q: solve the following diffrential c) x²(y+1)dx+(x²-1)(y-1)dy=0

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Q: Find the particular solution of 3x ydx – (x + y)dy = 0 y(1) = -2.

A: 3x2ydx-(x3+y3)dy=0M=3x2yN=-x3-y3My=3x2Nx=-3x2Since My≠NxTherefore, Non Exact diff. eq.Find…

Q: Solve the given DE y'= X - x 3 — 2y 3 3ху 2

A: We have to solve the differential equation

Q: Obtain the particular solutions of the following: (y-Vr² + y² \dx– xdy =0, y(0)=1 a.

A: Solution is given below:

Q: Find the complete solution of dy + dz = 3z'ydz

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Q: 4. Solve the given nonhomogeneous( or undetermined coefficient( O.D.E by variation of parameters (1)…

A: In the first step find the complementary solution of the given differential equation:

Q: Find the general solution of the following DE. xy(y')² + (x² + y²)y' + xy = 0

A: Here given the differential equation as xyy'2+x2+y2y'+xy=0 Replace y' by p, then xyp2+x2+y2p+xy=0…

Q: Use undetermined coefficients to find the particular solution to y'' + 5y' + 6y = 3e t %3D Y(t) =|

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Q: d'x +x=f(t), if x =x' = 0 for t = 0. Solve d?

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Q: 3. Find the complete solution of 2xdy – y(x + 1)dx + 6y³dx = 0

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Q: Solve the non-homo. D.E. 1.y" + y = 3e2x

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Q: r'ydx+(x* + x*y° + y*\dy = 0

A: See the details solution in below

Q: Find positive numbers x and y satisfying the equation xy = 21 such that the sum 3x+y is as small as…

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Q: Solve the non-homo. D.E. 1.y" + у%3D Зе2x

A: Differential

Q: ) Use the method of Undetermined Coefficients to find the general solution to the DE y" – 3y + 2y =…

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Q: Use separation of variables to find a family of solutions to the following PDE и (т, t) — с'и (т,t)…

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Q: Find the particular solution of -4y = 3x – 1 given that when x=0, y=0 and d2x dx dx II

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Q: 3. Solve the DE ty' + 2y = ont, 4. Solve dy dr 1+ y?

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Q: Solve the following Euler-Cauchy type equation: 1 (x² D² + 3xD+ 1)y = - 3xD+ 1)y = (1 – x)² ' d…

A: Given equation is, x2D2+3xD+1y=1(1-x)2 Take, (x2D2+3xD+1)y=0 Then assume, y=xn,…

Q: Ex: FIND A COMPLETE SOLUTION OF EQ. y" + 3y" + 3y' + y = 0

A: The given differential equation is y'''+3y''+3y'+y=0. Find the complete solution of the differential…

Q: Q2: find the general solution: (D* - DD')z = (x² – 2y)e" + sin (2x – y) •2

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Q: x²y" +xy' – 4y = 2x*

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Q: Suppose that the DE y"" (x) + 7y(x) =70 2³ +123 has a solution of the form y = Az³ + B Find the…

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Q: Is y = cīt + cf is the solution to y" – 12y = 0? Prove it

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Q: [dz dx (x+y+z)dy (c) CS imscarner

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Q: Use Secant method to find to find solution accurate to within 10 for the following problem. (i).…

A: Given function is  (i) f(x)=3xex Here x0=1, x1=2 f(x0)=f(1)=3(1)e1>0 f(x1)=f(2)=3(2)e2>0 Since…

Q: 4. Find the complete solution of xdy + (x³ – xy? – y)dy = 0 |

A: According to question,Given differential equation,x dy + x3 - xy2 -y dy = 0

Q: 4. Solve the given nonhomogeneous( or undetermined coefficient( O.D.E by variation of parameters (2)…

A: We have the given question,  This is a Euler-Cauchy Differential Equation of the form ax2y''(x) +…

Q: Obtain the general solution of the following: A. (D2 − 1)y = ex + 1 B. (D2 + 1)y = sec3x

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Q: Use the Regula Falsi method to find the first two approximations for the unique solution of x^5 − 6x…

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Q: Obtain the general and particular solution 4. xydx + (x² + y²)dy = 0

A: The given problem is solved below in detail.

Q: Find the complete solution of ydx + (x + y²)dy = 0

A: Let us consider the differentiable equation of the form Mdx+Ndy=0 If ∂M∂y=∂N∂x then the solution is…

Q: Consider the equation: ay" + by' + cy = g (t) where a, b, and c are positive constants. 1. If Y1 (t)…

A:

Q: Find the General Solution dy dr = y? – 3y²cos (x) 1.

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

Q: Given that y1 = 3x is a solution of æ°y" + xy' - y = x2 on the interval (0, 0), use the reduction of…

A: Concept - used the reduction of order

Q: (b) For the solution that satisfes v(0)1, sketch the solution curve and estmate the following v(0.5)…

A: (b) The solution that satisfies y(0) = 1 can be sketched as follows:

Q: 3. xdy - [5x*(x²+y²) +y]dx= /x²+y² (xdx + ydy)

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Q: Find a particular solution to y" + 16y = 24 sec(4t). Yp |

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Q: - Find the solution of the separable DE 2ydy = (x + 1)dx. a. y- +x x+c c y=x'+x+C d. y=x + 3x + C b.…

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Q: 3. Find the complete solution of (x²y+y³ – y)dx + (x³ + xy? + x)dy = 0 Hint: Expand and Simplify

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Q: Find two values of n such that y = enI is a solution of y" + y' – 72y = 0

A: Given differential equation,  y'' + y' -72y = 0 To find the solution of above equation in form of…

Q: Solve the non-homo . D.E. 1.y" + у %3D Зе2х

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Q: Solve: (D² + 5DD' + 6D²)z = (y – 1)e* + sin(2x – 3y) + 3x + y, where D =- and ax D' = y = 2 ду

A: Given partial differential equation is, This is a homogeneous partial differential equation with…

Q: 2 = 3x° (7 + y²) dx

A: Here equation is separable so w separate them and apply integration.

Q: Solve the bernoulli's equation x(6x^2−y−1)dy +2ydx =0.

A: The given Bernoulli’s equation can be written as:

Q: (1+ 4.x²)y" – 8y = 0 equation xo = 0 1

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.