Theorem: If A has a repeated real root λ with corresponding eigenvector K₁ then all solutions of X' = A X are of the form: W x ν = (*) -K et K₁₂ (te K₁ + e₁t W2 where (A - I) (B)- = K₁. Theorem: Let λ₁ = α + i ẞ be a complex eigenvalue of the coefficient matrix A with corresponding eigenvector K₁ = B₁ + i B2. Then all solutions of X' = A X are of the form: ()- That is: }) y = c₁ (B₁ αι cos ẞt - B2 sin ẞt) eat + C₂ (B₂ cos ẞt + B₁ sin ẞt) eat. |= c₁ (Re(K₁) cos ẞt - Im(K₁) sin ẞt) eat + C₂ (Im(K₁) cos ẞt + Re(K₁) sin ẞt) eat.

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: Solve y (e* + Inx) dx + (3 – y) dy = 0

A: The given ordinary differential equation can be written as:

Q: dy y = x-'(a² + x²)¿, solve for dx

A:

Q: - 2- Solve: (2x +1) a.) dx3 +2y 3e* dx %3D dx2 + 6(2x+ 1)+4y = (2x+1) [t= In(2x+ 1)] %!

A: According to our guidelines we can answer only one question and rest can be reposted.

Q: CALCULATE USING A HOMOGENOUS EQUATION. GIVE THE GENERAL AND PARTICULAR SOLUTION. SOLVE NUMBER 3 THE…

A:

Q: (xy^2- y^2+x-1)dx + (x^2y-2xy + x ^2+2y-2x+2)dy = 0 Start by using seperable equations.

A: given a differential equation,here need to solve this differential equation by seperation of the…

Q: y' = (x - 1)(y-2), y(2) = 4

A:

Q: Find / dy dx 174= √² y = √5 +1 and S=16x²= 2√

A: Note:-Since you asked multiple questions, according to our policy we can answer only first the…

Q: () Find the solution that satisfies Y(0) 1

A: We will find out the required solution.

Q: = 11. Solve x²yd²y + x dx² .2 dy dx - y)²³-3y² = 0.

A:

Q: Find/ S dy

A:

Q: + y = ty dt

A:

Q: Use a suitable method  to find the solution of (1-x^2)(1-y)dx=xy(1+y)dy

A:

Q: Solve y' = 12xy 2х, у(0) — 15 -

A:

Q: ( 3x²y + e' )dx + ( x³ + xe' - 2y)dy=0

A: We will first check whether given equation is exact or not ,then we find general solution…

Q: Solve the IVP: X' = AX, where -2 1 A = -5 0 3 -2 and -2 X(0) = -1 2

A: To find the solution of X'=AX where, A=−210−50003−2X0=−2−12

Q: x = y+ xe' dx

A:

Q: Find general solution of ODE   (x+y-1)dx-(x+y)dy=0 dy/dx = (x+2y-3)/(2x+y-3)

A:

Q: dy Q2) Solve x- 2y = x³ cotan 2x dx

A:

Q: Ex.: Solve dx dy 2- dt -x- e' dt dy dt dx +2. +y%3Dt.. dt versity-Civil Enginee & Num. A

A:

Q: (2t – 3)·e -t²+3t dt 3 2/Inx dx . X (2у-3)12

A:

Q: 7 0-3 -9 -2 3 18 0-8 y, y(0) = 2 3

A: Given y'=70-3-9-23180-8y Also given y0=23-1   To reduce to row echelon form and solve for constant…

Q: Determine the general solution: (dx/dt)A3 - (dx/dt)^2 - 4x = 0 Select the correct response: O y= c1…

A: Topic:- differential equations

Q: Use the exact techniques to determine the solution to (2y? + 2y + 4x2)dr + (2ry + x)dy = 0.

A:

Q: Solve the system [: 16 -36 dx dt 6. -14 with the initial value 13 x(0) 5 -5e^(4t)+13e^(-3t) x(t) =…

A:

Q: Solve the IVP dx -5 dt 4 = x (0) = = -4] -5 - x 8 ;] 2 Give your solution in real form. x1 = x2 =

A:

Q: Solve 2(ax+Y) dx + (3x +Y) dy =0 ,y) =2

A: SOLUTION-

Q: Solve dy/dx + 2y = 4, y(0) = 3 by one of the usual methods. Solve same the problem by Picard’s…

A: Integrating factor method for solving a differtial equation  Consider the differtial equation…

Q: Q9// find the general solution (sec³x + (cotx)y)dx + (Insinx)dy = 0

A: Answer and explanation is given below...

Q: Find the general solution to this exact equation: y + (2ty-e^(-2y) ) dy/dt = 0

A:

Q: The standard form of 3dy-xydx= 3y³e/3 by Bernoulli's ec 4x/3 dx 3 A dy ху = 3e**/3y3 dx 3 'x=…

A: