Question 15 Consider the following IVP: y" -3y' -10y = 1, y(0) = -1, y'(0) = 2 Find the general solution. 1 5t 14 -21 (A y(t) 35 10 13 12 -51 _ 13 ,21 10 у (1) 14 35 1 5 13 -21 © y(1) e 10 35 14 1 -Sr _ 13 21 D y(t) = 10 35 14 + B.

Q: Find the general solution of 2 4 4 X' = -1 -2 0 X. -1 -2

A: To solve the following problem

Q: Assume: (1) FIT calculated by percentage method and (2) Social Security 6.2% on $118,500; Medicare…

A: Based on the wage brackets provided, let's analyze how income tax withholding is calculated for a…

Q: 4ry" +2y' +y = 0. Solve using Frobenius

A:

Q: would you prove that the answers to the diophantine equation y^2-x^3=0 are the pairs (n^2,n^3) for…

A:

Q: 6, Solve the IVP 3w" -u'+ 2u0. u(0) = 2, u'(0)-0

A: The given equation is; 3u"-u'+2u=0, u(0)=2,u'(0)=0

Q: 3 2 y' у. -5 1

A:

Q: Find general solutions 17. y" - 4y = -12r² +6x-4; 18. y"+y+y = -13 sin(2x); 19. yy=e+xz; 20. y" - 4y…

A: 19)  We have given a differential equation ,  y'' - y = ex + x First we will find complementary…

Q: Given y = Vx – 2Va – 2; Find y'. - |

A:

Q: 4. Find the particular solution of xy' – 2y = -x; when x = 1, y = 5 C. y = x - 2x² d. y = 2x – 3x…

A: Given that: xy'-2y=-x; when x=1, y=5       NOTE: As per our answering guidelines, we can only answer…

Q: Find the general solution of the following Cauchy-Euler equation x²y" - 2xy' - 2y = 0

A: We have to find the general solution of

Q: Find the general solution of i = Ax, where A = .

A:

Q: y" - 5y' + 6y = 0

A:

Q: 3) Given that y₁ = ex is a solution to the ODE xy" + 2(1-x)y' + (x-2)y= 2e* Find a solution for y2

A:

Q: Let A 22 - (²²) 11 Find the solution of the problem: x), Y(0) = = - (8) -X Y' = AY +

A:

Q: 13 4e 6t -3t x; X 28 - 10 7e 6t 4 e 3t 13 4 13 -4 6t 4e |=x,' 28 10 28 - 10 7e 6t

A: The given question is solved below.

Q: y"+y' + (a) -5 x-b = 0, Xo = 2 is 5. (b)-3 (c)-2 d)-8 Q7) L(y") = a) s²L(y(x)) + sy(0) - y'(0) c)…

A: We have given the answer in the next step. Hope you understand that

Q: d tet dx 1+e* , xe" + e* – e 2x A (1+e*)? xe" +e* +e2« B (1+e*) 2 xe* + e2* (1+e*)? (1+e*)xe* – ¢2«…

A:

Q: 7) 3x +3e'x2/3+tx'=0

A: Given 3x+3etx23+tx'=0

Q: Create a matrix B that fits within the scope of Hermitian Matrices, write, and solve a linear…

A: Consider the matrix B with complex entries ( over C), then the conjugate transpose of B is defined…

Q: Use undetermined coefficients to find the particular solution to y"-4y-5y = ex (24 - 5x) Yp(x) =

A: To Find:Particular solution using an undetermined coefficient.

Q: B 2y (2x +3)'/2 (2x + 3)

A:

Q: 1 -~-² ( 5 (52² + 4) = = = √( ² ) 6' +4' sin2t.dt

A: As per the instruction, we will be answering the first question. For (1), We need to verify the…

Q: Find tha gmoral solution of gr - 7y' + My =1 0

A:

Q: r3 + y = Ty, then y = 32 3» ყ passos " 1 — 34 + ყ 3.72 O x - 3x² + y 3y² O 32 — y — 3g2 - lf

A: Given

Q: 26. y" – 6y' + 13y = xe3* sin 2x |

A:

Q: 2. Let AX = B with 2 1 1 3 ^= [₁ ²²² =²×²0 EJ A: 0 -3 -2 B X y ) 2 1 use the fact that 1 A-¹ = 2 -3…

A: We have to find the value of variable and verify them the result

Q: Use undetermined coefficients to find the particular solution to y"-2y+4y= 4t+7 Yp(t) =

A:

Q: 35) y+ y, =-5cos(2t), y+y, = 5cos(2t), y;(0) = y{(0) =1, y,(0) =-1, y,(0) = 1.

A: The solution is given as