Solve the IVP: ry'- 2ry 10x2, y (0) = 1 Oy- 3e + 222 4 Oy = 6e #= 5z = 5 Oy=-e + 5x + 27 Oy= - 5z - %3D

Q: 3. Find (6-+- vē)dt Vy 4. Find S- dy (4-yの?

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Q: Solve for the particular solution of the non-homogeneous DE. y'' + y = 2x

A: Solve for the particular solution of the non-homogeneous DE. y'' + y = 2x

Q: (x2 + 3 y9 dx - 2xy dy

A: It is homogenous differential equation.

Q: Obtain the general solution valid near the origin: х(х-2)y1+2(х-1)у - 2у %3D0

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Q: Use separation of variables to find an explicit solution. xyy' = 2xy + y?

A: Idea: after separating x,dx and y, dy terms together. we take integration on both sides . after…

Q: In the process of using an "auxiliary equation" to solve a homogeneous DE, the final result can be…

A: Depending on the type of roots of the auxiliary equation, there will be 3 different types of…

Q: y" + y = 2x

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Q: Solve: dy 6- y") +. onn 13-1 Ordineiy Dibgerential equation

A: The solution of the differential equation can be found with the help of the separation of the…

Q: a) Solve y' = 3x² + y, y(0) = 4 by choosing step length 0.1 for y(0.2) by Euler's improved method

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Q: y(4) + 3y" + 2y = 0

A: We have to solve given differential equation.

Q: Use variation of parameters to find a general solution: y(3) – 4y = et.

A: Given differential equation: y3-4y'=et         ...(1)

Q: y" + y = 2x

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Q: Solve the initial value prol dy + 8, y(1) = 3 dx y%3D 4 Jx +8x 19 4 Oy=Vx + 8x - 6 Oy=-- - 8x- 6

A: Explanation and solutions is given below....

Q: dy-Hy-5 te %3D xp

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Q: Solve for x, y, z and w by Gauss elemination Method. Given: 12x-8y+6z+10w=26

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Q: Use the Adam-Bashforth method of the second order to solve the second equation y’=y(x+y) when h=0.1…

A: Given differential equation is y'=y(x+y), step size h=0.1 with initial condition y(0)=1 Let x0=0,…

Q: Find the general solution of the DE: dx 6- dt2 + 12- - 8x = 0 %3D - dt3 dt

A: Given ODE is d3xdt3-6d2xdt2+12dxdt-8x=0

Q: use Separation of Variables to find the general solution. yy' = x

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Q: Find the general solution of: ydx — х*dy 3D0. || -

A: Use variable separable to solve the differential equation. Note: We are allowed to solve one…

Q: y" - 5y' = x - 2, when x = 0, y = 0, y' = 2

A: We have to solve the given differential equation.

Q: By using linear method, solve dy %3D

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Q: Solve (D2 – 2)y =0 O a. y = cqevZx + c2e¬vZx O b.y= "(c,cos/2x+ c,sin/2x) O c.y = cqevZx+czxe¬VZx O…

A: The equation D2-2y=0 represent y''-2y=0 . Consider the solution of the differential equation is in…

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

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Q: Solve for the particular solution of the non-homogeneous DE. 2y'' +y' = 3

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Q: Use Variation of Parameters to find a particular solution to the non-homogeneous equation y′′−2y′+y=…

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Q: y" + y" = 3

A: Solving the given third order differential equation

Q: Use the separation of variables method to solve 4UTr H Utt: 00 uz (0, t) = uz (2, t) = 0 u(x,0) = x,…

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Q: Integrate  zex^2 + y^2  over the cylinder  x2 + y2 ≤ 25, 2 ≤ z ≤ 5.

A: Integrate zex^2 + y^2 over the cylinder x2 + y2 ≤ 25, 2 ≤ z ≤ 5 as follows.Here, x2 + y2 = 25 and…

Q: Find a homogeneous LDE with constant coefficients that has y=-1+3x²e* as a particular solution.

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Q: 1- , L, v² e*dydx 2- S S マーーー ydxdzdy a>0

A: Explanation of the solution is given below...

Q: Solve the IVP dy/dt + 2(t + 1)y^2 = 0, y(0) = −1/8

A: To solve the IVP dy/dt +2(t+1)y²=0, y(0)=-1/8

Q: 2y" + y' = 3

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Q: y" + y = 0, y(0) = 0, y' (5) = 2

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Q: Solve using the integrating factor by inspection  (2x²y - y²x + yx) dx + (3x³ - 4x²y + 3x²) dy = 0…

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Q: 1. y(4x + y)dx – 2(x² – y)dy = 0

A: We will first convert the equation to exact and then solve

Q: Obtain the general solution valid near the origin: 2y" + 9ху' — З6у %3D 0

A: Power series solution of the differential equation

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

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Q: Solve the DE using Linear First Oder Method: y +yx = x - 3. if y(0) = 2 %3D

A: Given y'+yx=x-3   if y0=2 To find the general solution

Q: 2. x (х — 2)у" + 2(х — 1)у' — 2у %3D 0 |

A: Power series solution of the differential equation

Q: ydx+(2x+3y)dy=0 solve by using homogeneous equaations

A: We know,∫dxx=ln(x)   Given differential equation, ydx+(2x+3y)dy=0 ⇒dydx=-y2x+3y....(i)

Q: general

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Q: y +y² – 1 = 0, Yı = 1

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Q: Obtain the solution using Integrating Factors Found by Inspection 2x 5y ′ = y(3x4+y2)

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Q: Solve (x² - 4xy-2y²) dx + (y² - 4xy - 2x²)dy = 0 By using the method of the exact equations 1-…

A: The given problem is to solve the given differential equation by using the method of the exact…

Q: dz az %3D Jsing separation of variables method, solve "+ = (x+ y)z ду

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Q: Obtain the general solution valid near the origin: x(х — 2)у" + 2 (х — 1)у' — 2у 3D0

A: The differential equation has singularity at the origin. So we find the solution by Frobienius…

Q: Use variation of parameters to obtain the general solution. y''+4y = 4 sec2x

A: The given differential equation is; y"+4y=4sec2x.

Q: dy/dx=x2+3y2/2xy

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Q: y' = y sec

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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.