Consider the initial value problem y+(2+2) = 0 with y(2) - 3 (a) Show that this DE is not exact. (b) Use the integrating factor / − y to solve the IVP implicitly.

Q: Use undetermined coefficients to find the particular solution to y'' – 3y' + y = 4t2 + 6t + 5

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Q: Solve the system d = dt with a1 (0) = 1 and æ2(0) = -1. %3D

A: The given system of differential equation: x1'x2'=   0-1-1   0 x1x2+t0  ;        x1(0)x2(0)=1-1

Q: Consider the following (x²-3x+1)y" -(x²-x-2)y'+(2x-3)y=0 on the interval I = (3,00) Verify that Y₁…

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Q: (x)= e°2× (x-1) us

A: Here The second method gives the correct result for an initial guess of less than one.

Q: (B) Find the general solution of x²y" - (2a-1)xy' + a²y = x²+¹ where a is a constant. Good Luck

A: This question is about ordinary differential equation.

Q: x²y" + 2xy' – 2y = 0; x > 0; y = y(x) (1) 3. Determine if the two solutions in Questions 1 and 2 are…

A: The general form of a second-order homogenous linear differential equation is given by…

Q: 2x2-3х-1 -dx (x²+9)(x-5) E. Integrate:

A: Let's integrate.

Q: Solve the following PDES by separation of variable metho (i): u +U, = 0 (ii): y'u, –x’u, = ди (iil)…

A: (i) uxx+uyy=0   ...i solve the PDE using separation  of varaible let u=XxYy differentiate with…

Q: Solve the following IVP: X' = AX + f(t), where 2 -1 A = 3 -2 and X(0) = ( : -3 2 f(t) 10t ||

A: First we need to find the eigenvalues and eigenvectors of a then find the complementary solution of…

Q: 3 then the integrating factor is ax (a) –3x (b) -3y (c) e 3x (d) e Select one

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Q: Find the general solution of (1+ x²)y' + xy = x=1(1 +x²)-/½

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Q: * - x(t) + 5ÿ(t) = t; ÿ – 4y(t) – 2x(t) = -2; y(0) = ÿ(0) = x(0) = ¿(0) = 0 %3D %3D

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Q: Consider the following initial value problem 3 3 6y" + 6y(x′)³ +48 (v′) ³ = 0, 3(0) = −5, 3/(0) = 27…

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Q: (D² − 1)y=e*(x² + 1)

A: THE HOMOGENOUS EQUATION IS , D2-1y=0 SO, THE AUXILLARY EQUATION IS, D2-1=0⇒D=1,-1 THE HOMOGENOUS…

Q: Q/Solve the following initial - Value Problem: хе x ex³dx + (x³²-1) dy=0

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Q: Use undetermined coefficients to find the particular solution to y'' + 2y' – 4y = 2t + 2 Yp(t) =

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Q: 23. Find the general solution of x (x 2)y" – (x? – 2)y' + 2(* - 1)y = 3x²(x 2)°e*, %3D

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Q: Section EXERCISE 8. dy dr Find the general solution of (2r-v) = 2y - 2y-

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Q: 1) Find the general solution of the equation x³y"" - 2x2y" - 4xy' + 8y = x² + lnx.

A: In this question we will find the general solution of the differential equations.

Q: 27. у" — 2у - 2y' 8xe2x. %3D

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Q: SOLVE BY INTEGRATING FACTOR METHOD (3xy + 2 c05 (4) dx + (x²-xaen (y)) dy = 0)

A: (.) Given differential equation is,     (.) Method of integrating factor: If a first order…

Q: 2e* xy" - (2x + 1)y' + (* + 1)y %3D * ond ex ore linearly indenerndent

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Q: 25. Find the general solution of (sin? x)y" – (2 sin x cos x)y' + (cos? x + 1)y = sin' x,

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Q: Consider the following equation: x?y" + 2xy' – 2y = 0; x > 0; y = y(x) (1) 1. Verify that y, (x) = x…

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Q: 24. Find the general solution of (2x + 1)(x + 1)y" + 2xy' – 2y = (2x + 1)², given that y = x and y =…

A: using variation of parameter

Q: 3. Determine whether the method of separation of variables can be used to replace uxx+2uxt+ut = 0 by…

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Q: Question 4 Let g : R→ R be differentiable on R such that g is contimuous on R. g(7) 1. g(12) e, and…

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Q: (x - y)y' - 2y + 3x + == 0 ; y(1) = 5 + X² = 0 X

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