y = 0, is: %3D The general solution of y +xy +9x-4 Oa C,(3x) + C,Y,(3x) Ob C,XJ,(3x) +C,xJ_2(3x) Oc C,XJ,(3x) + C,xY,(3x) Od C,J,(2x) + C,J_3{2x) O e C,J,(3x) + C, Y,(3x)

Q: Determine the particular solution. (xy)dy – (3x² + y²)dx = 0; Y(1) = 1 O 3ln(x) + 12 = 1²² 2x² O…

A: Let's solve differential equation.

Q: What is the general solution of xy(xy³ – 1)dx + x²(1+xy)dy=0? A 2x°y³ -3x²= Cx² 4x³y? +3x?= Cy ©…

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Q: Exercise 5 Using the method of variation of parameters, the particular solution Yp for y" + 3y + 2y…

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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: 2x 3x The DE whose general solution is given by y = x²+c,e*+C2e is © y" - 5y' + 6y = 6x2 – 10x +2. |…

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Q: Q: Find the solution of x, y, z by using Gramer's Rule. 3x + 2y - z = 1 x- y+ 5z = -2 2x + y = 3

A: The given system of equation is  3x + 2y -z =1 x - y +5z =-2 2x +y =3

Q: a) 2xy dx+(1+x²)dy=0 b) y'+(4/x)y=x* ------by exact method ---by linear method

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Q: 2x4 +3x2 – 1 Rewrite dx as integral of sum of partial fractions. (x³ – 4x² + 5x)? - B + E |dx x+1'…

A: we can reduce into partial fraction

Q: 4. Find the general solution of (x³ + y³) dx = 3xy? dy A. -3x3 + 2y3 Cx B. 7x3 + 2y3 = Cx C. -6x3 -…

A: According to question, Given differential equation, x3 + y3 dx = 3xy2 dy

Q: The integrating factor of the equation (xlnx)y' + y = 2lnx is || Select one: a. ex O b. Inx c.…

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Q: 8. Find the general solution of (x2 + y2 + 1) dx + (x2 – 2xy) dy = А. х2 - у? - ху — 1%3D Сх В. х2 +…

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Q: Find the general solution of (xe +y)da – cdy = 0 %3D

A: Given differential equation is xeyx+ydx-xdy=0 we can write it as dydx=yx+eyx             (1) which…

Q: Obtain the particular solution of (3x2 - 2y2)y' = 2xy; x =0, y=-1.

A: We have to solve

Q: (b) Use Gaussian elimination to find the values of x, y and z: x+2y+3z=10 -x+y+z=0 y=z=1

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Q: What is the general solution of xy(xy³ – 1)dx + x²(1+xy)dy= 0 ? A 2x°y3 -3x2= Cx? B 2x³y5-3x² = c ©…

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Q: Q Find the solution of x, y, z by using Gramer's Rule. 3x + 2y - z 1 x- y+5z = -2 2x + y = 3

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Q: y-z z-x x-y General solution of p +q =*y yz xy

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Q: Find the general solution of (x³ + xy2 + y)dy + (x²y + y³ + x)dx = 0 %3D xy + In(x² + y²) = c 2xy +…

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Q: Find the general solution of (x + y – 1)dx + (2x + 2y + 1)dy = 0. a. x + 2(x + y) + 3 In(x + y + 1)…

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Q: + To solve dx using the method of partial fractions, we write it as x(x2 +6x + 10)² A B(2x +6) + C +…

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Q: What is the general solution? d3x d?x – 4x = 0 dt3 dt2

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Q: Find the general solution to(D5 - 2D³ – 2D2 – 3D - 2)y=0 O y= e-X(C1 + C2x)+ C3e2× + C4cosx+ C5sinx…

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Q: the general solution of yv1+x²dx + x/1+ y?dy = 0 using variable separable method. 3. Obtain X-

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Q: 3 9 dx dt -1 -3 2 and x(0) 4 ||

A: In the question it is provided a system of differential equations:

Q: (With Solution) The particular solution of x dy - y dx - (1 - x²)dx = 0 when x = 1, y = 3 is a. y +…

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Q: What is the general solution of xy(xy5 −1)dx + x²(1 + xy5) dy=0 ? A 2x³y³-3x²= Cx² B 2x³y5-3x²=Cy²…

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Q: Find the solution using Gaussian elimination: w + 2x − y + z = 6 −w + x + 2y − z = 3 2w − x + 2y +…

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Q: Use the method of integrating factor to solve the linear ODE y' – 3y = 1-e-2".

A: Given: y'−3y=1−e−2x

Q: - using homogeneous method, show that the solution of the 1 equation: x -3y ²+2xy 2_3y dy -=0 is:…

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Q: 9. Find the general solution of y(2x + y²)dx + x(y² – x)dy = 0

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Q: The general solution of (y- 1)dx - 2(x+y+1)dy= 0 by CL2V is A (x-2y)= c(y- 1)? B (x+2y)= c(y- 1)2 (x…

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Q: using the the Classical 4" - order Runge-Kutta Method (RK-4) x+1 y = y, y(1) 1 1sxS 2, h = 0.5 If…

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Q: Particular solution of y' = x+xy²/4y, y(1) = 0

A: Given differential equation- y'=x+xy24y   , y(1)=0 We need to find particular solution of the given…

Q: The particular solution of x dy - y dx when x = 1, y = 3 is a. y + x2 – 1 = 3x b. y + 2x2 + 1 = 6x –…

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Q: dy - Find the general solution of Y +2 = 3x²y² dx A. 1/(xy) = -3(x³/2) + C B. 1/(xy) = -3(x²/2) + C…

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Q: given: v=(3t - x)e-2t 1. find (d2v)/(dt2) 2. find (d2v)/(dtdx) complete solution

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Q: y =-x² +2x+7 y =-2x +2 → Solution(s): %3D S y = x + 2x –3 %3D y= 2x+1 %3D → Solution(s):

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Q: The general solution of 2y" -xy'+ (x - 24 ly = 0, is: OaC,xJ,) + C,xJ_(2) OcC,,(3) + C,xJ_(3x)…

A: The given equation is  x2y"-xy'+x2-24y=0                                  (1) The differential…

Q: Find the value of x, y and z using Gaussian Elimination Method: ax + y + z = 1 x + ay + z = 1 x…

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Q: A particular solution of y -2y + y e':

A: Given differential equation:     y'' - 2y' +y = et We use method of undetermined coefficient to…

Q: Find the general solution to(D5 - 2D3 -2D² – 3D – 2)y=0 O y= e-X(C1 + C2x) + C3e2X + C4cosx + C5sinx…

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Q: 4. Find the general solution of (x3 + y³) dx = 3xy² dy = Cx = Cx А. -Зx3 + 2yз В. 7x3 + 2у3 С. -бх3…

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Q: What is the general solution of xy(xy³ −1)dx + x²(1+xy5)dy=0? (A) 2x5y³-3x²= Cx² B 2x³y5-3x2= Cy²…

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Q: D³y = 0 ; x = 1; y = 1; y = 3; y" = 2

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Q: 4. Are y1 (x) = e*and y2(x) = x + 1 solutions of the D.E. xy" – (x + 1)y' +y = x2. Are y1(x)…

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Q: Appropriate form of particular solution of y4) – y(3) = e3x + x is (a) y, = Ae3x + Bx* + Cx3 + Dx? +…

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Q: Determine the value of C if f(x,y) = C is the solution of (x+ 2y-3)dx+(x+2y+1)dy3D0 for x=94 and y=…

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Q: Obtain a particular solution for + + +y = x³ + 2x + 1 dºy, d²y dx4 dx²

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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.