3. Find the general solution to: xi = 4x1 + 2x2 + 3et x2' = 2x1 + x2 + et. %3D

Q: dy 4x2-х-2 : У(1) %3D 1 dx (х+1)(у+1)

A: Explained below

Q: xarctanydx + dy = 0 2(1+ y²)

A:

Q: 4x Compute (2x + 4yz) dz dæ dy 1

A:

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

A:

Q: (у — ӕ + хусotx)dx + zdy — 0 y(0)= 3

A:

Q: 2. Using the variation of parameters, find the particular solution of (D² + 1)y = sec x

A: By the method of Variation of perameters

Q: Using Trapezoidal method √²³x² dx for n = 4 is equal to

A: The trapezoidal rule works by approximating the region under the graph of the function f(x) as a…

Q: 1.Solve the given problem W = f(x, y, z) = 3x²y+ yz² + 2z³ fxis equal to ? fyis equal to ? fzis…

A: Follow next step

Q: Find the complete solution of the given DE using the Method of Variation of Parameters: y" + 4y asC…

A:

Q: x°y"+ 2x?y"+ xy'- y=0

A:

Q: fin the general solution of (x+2y-4)dx - (2x+5-y)dy=0

A: Please see the below picture for detailed solution.

Q: Find the General solution Use method of undetermined coefficients. 1. (D² l)y=ex (2sinx + 4cosx).…

A: To Find: the general solution using the method of undetermined coefficients   1. D2-1y=e-x2 sin(x)+4…

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

A:

Q: (r²+y + y³) dx – x dy=0

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

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

A:

Q: 3. 2y" + у' - 3 А. 3 В. Зх C. 3x D. x?

A:

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

A: To find the particular solution for the given DE.y''-5y'=x-2, when x=0, y=0, y'=2

Q: 2 ydx + x(x In y – 1 )dy = 0 %3D

A: Given that: 2ydx+x(x2lny-1)dy=0

Q: Solve by the addition method: 11x + 13y = 9 1 lx + 26y = 13 O A. No solution %3D 3 4 OB.

A: We need to find (x,y) here which satisfy both equations

Q: 2. (D² - 3D + 2)y=1+x

A: The given differential equation is;  (D2-3D+2)y=1/(1+e-x).

Q: I. Find the general solution of the following: 2x* 1. dx 2.d = xy 3. dy = (6e³x + 1)dx

A:

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

A:

Q: x²dx + y(x-1)dy = 0 %3D

A: We need to find solution of differential equation.

Q: y" – 4y' + 8y = x², y(0) = 2, y'(0) = 4

A:

Q: The solution of DE.s divided into complementary solution and particular solution. * O True False

A: Consider a nth order differential equation dnydxn+dn-1ydxn-1+dn-2ydxn-2+.........................+y…

Q: 4. x(xy – 1)dx + dy = 0(Non-exact)

A:

Q: 2y" + y' = 3

A:

Q: 4. Solve for Y (s) given ty" + y' + ty = 0 y(0) = 0 %3D

A:

Q: Obtain the general solution unless otherwise instructed 1. arž -y = 10sin²x dx² SUMMARY OF ANSWERS…

A:

Q: 2. у" — у' — х %3D 0

A: To solve the given differential equation.

Q: ydæ + (x'y4 – 3æ) dy = 0

A:

Q: (8) 2xy = x2 + 2y² = x² dx

A: As per our guidelines we can answer only 1 question so kindly repost the remaining questions…

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: Check for exactness and obtain the general solution. 1. -x(4y3 – 3xy – 6)dx – (6x²y² + 1- x³)dy = 0

A:

Q: 3. Find the general solution of 2x + 2xy² y + 2x2v dx

A: By see this solution below

Q: Find the general solution to the DE using the method of Variation of Parameters 8 у" — 4у 3D e 2x +…

A: Introduction: The formula of the particular solution by the variation of the parameter of the…

Q: Solve the ruiftlal -value problem sy'-3 y =0 1 yl0) = - | y'(0) = 24 ニ ylo)= ? %3D

A: The differential equation is given as 2y''+5y'-3y=0 The corresponding auxiliary equation is…

Q: the general solution of DE x2 dy/dx=4x2+7xy+2y2

A:

Q: Determine the general solution for the following: 1. ( 6x2 - y +3 ) dx + (3y² -x - 2) dy =0

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: 8. Solve for x and find value of SU. 10 U. V. D 4 T. 3x +15

A: Given data: UT=4, US=3x+15, UV=10 and UD=x+6 If chords TS and VD intersect externally at point, U…

Q: (ylny – e¯xy)dx + ( + xlny) dy = 0

A: Solution :-

Q: y™ -2y = 0 %3D

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

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

A:

Q: ydx + x(Inx - lIny - 1) dy = 0, when x = 1, y = e %3D

A: Given :     ydx+xlnx-lny-1dy=0,        when x = 1 , y = e that means y1=e

Q: Use the method of Variation of Parameters to solve the following DE: у" — у %3D2х2 —х— 3.

A:

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: Find the general solution of y"+25y=sec(5x)

A: