x + y + z + w = 6 2x + 3y – 3x + 4y + z + 2w = 0 x + 2y - z + w = 6 w = 12 %3D %3D

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: Tkrit University Civil engineering Department Third Stage Eng. Anal & Num Meth. Dr. Adnan layed…

A:

Q: (2x + 3)y' = y + (2x + 3)/½ a. y =- In(2x + 3) + C b.y = (2x + 3)In(2x + 3) + C c.y = (2x + 3)(In(2x…

A: The solution of first order linear differential equation of the form y'+P(x)y=Q(x), is…

Q: 1. (x+ 2y) dr-3y dy = 0 O x-6xy+8 xy'-3 y c O 3x -8ry + 6 xy'- y = c O x+ 3xy -4 xy' + 3 y c O+3xy-6…

A:

Q: a) x'y" - (2x- 1)xy' + (x- 1)y (x+ 1)e2x. %3D b) x2y"-2(x2 +x)y' + (x2 +2x + 2)y = x'e2x %3D dzy c)…

A:

Q: 1. y' – 5y = e5x ;y(0) = 0 2. y" + 4y = 0;y(0) = 2, y'(0) = 2 %3D %3D

A: In the given question we have to solve the given differential equations by using the Laplace…

Q: 1. (16x y² etxy + y sec² (xy) – 2x + 3y) + (16x² y e*xy + x sec²(xy) + 3x)y' = 5

A: Given: 16xy2e4xy+y sec2xy-2x+3y+16x2ye4x+xsec2xy+3xy'=5

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

A:

Q: y- 2x = 3y - 2 %3D Oz= 3yIny +1+Cy Oz= 3lny +1+ Cy Oz = 3y Iny +1+C Oz= 3y Iny + Cy

A:

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: 6. 13. a +1 =; 14. t- 3 15. x + 1 1 x+2 x+ 1 %D - %3D 16. y y2 +4 2 1 y + 2'y - 2 y² – 4 17. d +4 d2…

A: As per our guidelines, i can answer only one question.

Q: 4) y" – 2 y" – 5 y' +6y = e 2x %3D 3x -2x 1 2x Ygenel = Cje* +cze³* +Cze %3D - 4

A:

Q: y"+4y'+4y=(3+x)e-2x, y(0)=2, y'(0)=5

A:

Q: (b) y = e, y = ²x, x=0, x= ln 2 1 (c) x = =, x = 0, y = 1, y = e Y (d) y = 5x - x², y = x (e) y =…

A: Using vertical strip

Q: Edx rB(2x+2) x2+2x t2 D(2x +2)dx (x²+2x+2)² Cdx (x²+2x+2)° (キャ9x+9×+x-x)dx (x-1)(X*+2x +a)* Adx x+…

A: Please see the below picture for detailed solution.

Q: æ' = 2) 4e x + %3D -4 3 2e er the associated homogeneous system

A: Given, x'=-12-43x+4et2e2. Find eigenvalues corresponding to the matrix A.…

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

A:

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

A:

Q: y' + yv1 + t4 = 0, y(0) = 0 y' + ycos(e') = 0, y(0) = 0 t3y' = 2y = 0, y(1) = 0, t >0

A: Let us solve the ODE in the next steps.

Q: Solve the equation y' = x^3 + y^3 / xy^2 fraction homogeneous first order ODE set v= y/x

A:

Q: x² + y² = (3x² + 2y² – x)², (cardioid) 0, y 0.5 -0.5 0.5 1 -0.5

A: Giv:    x2 + y2 = ( 3x2 + 2y2 x )2     Point: ( 0 , 1/2 )

Q: 6. y" – y – 6y = 0, y(0) = 1 e y'(0) = -1. 7. y" – 2y' + 2y = 0, y(0) = 0 e y'(0) = –1. %3D

A:

Q: 2 3 6 + k dt V4 – t2 4+ t2 |

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

Q: 5. y" – 3y' +2y=0; y1 =e*, y2 = e2x; y(0) =1, y'(0) =0 %3D -

A: Here is the solution:

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

A:

Q: %3D iv) if zy = (x)-1 then z, + Zy = b.x+y c.-z (x+ y) d.z² (x- y) a.x-y

A:

Q: A closed biological system populated by M number of prey and N number of predators is given by dM =…

A: Given that, dMdt=a(M-MN)dNdt=b(-N+MN) Where a=1 year, h=0.2 year , M(0)=0.1, N(0)=1. Take,…

Q: Appropriate form of particular solution of y(4) – y(3) = e3x +x is %3D (a) yp = Ae3x + Bx* + Cx³ +…

A:

Q: x³ +x² + x + 3 dx. J (x² + 1)(x² + 3)

A: Given,           ∫x3+x2+x+3x2+1x2+3dx

Q: х+у+2z %3D0 Solve x - у + z %3D —1 2х + у +z %3D2 by Gaussian elimination. а. (1, -1, -1) b. (1, 1,…

A:

Q: 1 (a) y = x-4 (b) y = x-5 (c) y = 2x Xー -2 -x + 2x-4 x-1 のy= x -4 (d) y = x-1 (e) y = x'(x-2) x-1 x…

A:

Q: Find the solution. xy'+ xy = 1 - y, y(1) = 0 A y = x-'(1 – e!-") y = x-2(1 + e'+*) © x=y-'(1 + e'-1)…

A: Given differential equation is xy'+xy = 1-y, y(1) = 0

Q: A. y = 2e* – x – 1 B. y = 2x° – 2x – 2 C.y=e²x+x – 1 D. y = e* + x + 1 f) xy' = 1 А. у %3 4 +x Inx…

A:

Q: 1) y"- 3y"+3y'- y = ť°e' ; y(0) = 1, y '(0) = 2

A:

Q: Find the general solution of the given system. dx = 4x + 5y dt dy = 10x + 9y dt

A:

Q: 2 (2y² + 5xy 4 Ο α. χ' (y² + 2xy = y + 2) = C O b. x4 (y² O 2y + 4) dx + x (2x + 2y − 1) dy = 0 - -…

A: The given differential equation is; 2(2y2+5xy-2y+4)dx+x(2x+2y-1)dy=0.

Q: 3 [² [v³ – y³]³ª a Jo ² dy

A:

Q: 2x4 + 3x² – 1 (x² – 4x² +5x)? B(2x- 4) + C Rewrite dx as integral of sum of partial fraction D(2x-…

A: Here we have to apply partial fraction.

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

A:

Q: roblem. y" – 2y' + 2y = e-; y(0) = 0, y'(0) = 4 %3D

A:

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

A:

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: 5x² – 7x +8 b) | dx (partial fractions) (x - 1)(x² + 1) .2

A:

Q: , у"+ бу'+ 9у 3D 0; x = 0, y = 0 and x = 0, y' = 3 = Ans. y=3 x e-3*

A:

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)…

A:

Q: Solve -) y''-y'- 2 y = 6 x e2x - 2 e*, y (0) = 1, y' (0) = 1 %3D y''- 2 y'+ y = x (e - e*), y (0) =…

A:

Q: x+y=z=6 3x - 2y + z = -5 x + 3y2z = 14 Solve value of x, y and z using LU Decomposition Method

A:

Q: Obtain general solution of the D.E. y' + (1/3)y = e%y4

A:

Q: Consider a person who invests in AAA-rated bonds, A-rated bonds, and B-rated bonds. The average…

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.