equakan ,yy= xe Solve the ditferen fal with initial condition yl0) =-2

Q: O Solve y' = x + y + xy, y(0) = 1 by choosing step length 0.2 for y(0.4) by Euler's modified ethod

A: Given y'=x+y+xy, y(0)=1 Take f(x,y)=x+y+xy, Using the euler formula, Since it is given that h=0.2.…

Q: 3. Solve the particular solution (D² + 3D + 5)y = 5e¬*sin2x using D- operator method.

A:

Q: Use Euler's method to approximate the solution to y' = y + 2t , y(-1) = -1 on the interval [-1, 1]…

A:

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

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

Q: Solve for all possible solution in the equation y^2 + y = x + Inx + e^y - x^2, using Secant Method *

A:

Q: x°y"+ 2x?y"+ xy'- y=0

A:

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

A:

Q: Doesn't this solution just ignore the initial height of 3 ft? So shouldn't the answers be slightly…

A: You are right here initial height have to be consider

Q: t with y(0) Solve y + 5y ing %3D 4 express- the particular solution as a convolution.

A: In this question, we have to find the particular solution of the differential equation by help of…

Q: Determine the interval of validity for the solution of the following IVP without solving it. (t2…

A: Given: t2-9y'+2y=ln20-4t, y4=-3 To Determine: Determine the interval of validity for the solutions…

Q: Sc ot'(3y)dy

A:

Q: Use variation of parameters to find a particular solution of the DE y/" – 4y + 4y then write down…

A:

Q: 3. Show that the equation (6xy – y*)dr + (4y + 32² – 3ry²)dy = 0 %3D is exact. Hence solve the…

A: Given that  The differential equation is  To solve the differential equation with intial condition

Q: Solve using Euler's Method dy=sin(x + y)- e*,y (0)-4, h-0.1

A:

Q: Find solutions using Exact Equations 5. Solve (2t3 + 3y)dt + (3t + y – 1)dy = 0

A: Firstly Compare given differential equation with Mdt+Ndy then find the exactness of equation and…

Q: 1 Oy' = %3D xsiny+2sin2y

A:

Q: (r²+y + y³) dx – x dy=0

A: →∫1a2 + x2dx  = 1atan-1xa→ddxuv = udvdx + vdudx

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

A:

Q: 5. Solve the 2nd- order differentinl equation: d'y dy dr +2 +y=e24 CS Scanned with CamScanner

A:

Q: Solve using Crámer's Rule. X + 2y + = 2 3z = -10 y 2x +2y %3D 3= IL || ||

A: x+2y+z=2 y-3z=-10 2x+2y=0

Q: Solve for all possible solution in the equation y^2 + y = x + Inx + e^y - x^2, using Secant Method

A: We have the following equation in two variables : y2 + y = x + ln(x) + ey - x2   As there are two…

Q: Use 4t order Runge-Kutta Method to solve dy = y' = x+y, y (0) = 1 & Y(2) = ? Use h = 0.5

A:

Q: (y+x*y²) dx +x dy = 0 5.

A:

Q: 3ox'y 0 has difruential equation d ftaential equation mily of solu tions given by hos a ane…

A: For the given differential equation, the family of solutions is given as.

Q: Y, = Ax² is particular solution of y' + y" = 1 for A = %3D

A: Here, yp=Ax2yp'=2Axyp''=2Ayp'''=0

Q: How do I solve this Bernoulli equation using P(x), Q(x) and n as well as u(y)?

A: First, we write it in form of Bernoulli Differential equation.

Q: Solve the Bernoulli's DE: 2x3 y = y(y? + 3x2). %3D

A:

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

A:

Q: 1. y' + 2y = x²y³ .2.3

A: Given problem:- solve the given differential equation y' +2y=x2 y3

Q: Solve the @iven dif frerenticul equation uning the variables method of seperatio n of dy 4y+3

A:

Q: 2 ydx = 3xdy; when x = -2, y = 1 Ans. y = (x/2)3

A: Given: 2ydx=3xdy ; x=-2, y=1   We know that; ∫1ax+bdx=1alnax+b+C

Q: 8. Using the Runge-Kutta method of the fourth, solve y" = y + xy', y(0) = 1, y'(0) = 0 to find…

A: We take y'=z the Given equation is y''=y+xz,y(0)=1,y'(0)=0,y(0.2)=?…

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

A: Power series solution of the differential equation

Q: (D* – 4D³ +14D² – 20D +9)y = 0 - -

A:

Q: Solve for the general solution of equation (4), d²X + B²X(x) = 0 dx? Express the general solution in…

A: This is a problem of IV.

Q: 2. Find te gunural soiUtion of 2

A:

Q: 2. (6x + y²)dx + y(2x – 3y)dy = 0

A: In this question, we need to check whether the given equation is exact or not and then find the…

Q: x²- y2)dydx a.

A: Solution :-

Q: 42. y" + 4y = sec² 2x

A:

Q: y +y² – 1 = 0, Yı = 1

A:

Q: y' = e2/y, y(0) = 1, 0 st< 2, h = 0.5 %3D

A:

Q: 2ste-tds + (s²e-t – t)dt = 0

A:

Q: 46. y" +y = Itsin z

A: Consider the given differential equation: Here the objective is to find the solution of a given…

Q: y™ -2y = 0 %3D

A: Given the differential equation y''''' - 2y'''' = 0. Auxiliary equation is m5 - 2m4 = 0

Q: Solve for the Bernoulli's equation -- ses 2ds = 5t³s3 .33 %3D dt

A:

Q: Obtain the general solution valid near the origin: 8x?y" +10xy' -(1+x)y=0

A: Power series solution of the differential equation

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: From the particular solution of the DE y" + 2y' + y = x at x = 0, y = - 2,  y' = 2, obtain the value…

A: