QUESTION 17 (x() If X= x2(t) is solution of the IVP X =0 1 0 X, x(0) (0 4-4 then x1(t)+x2(t) + x3(t) = Oa -3e'+1 Ob-Se' +1 Oc Se' +4 Oa-3e' Oe -3e'+4

Q: show that 2sin(x)3cos(x) = x has 3 solutions

A: 2sin⁡(x)3cos⁡(x)=x

Q: (2x+1) (x+1) y"+2xy' - 2y = (2x+1)- A solution of the homogereous Jorm is → y= (x+1)-1 Find the…

A: The differential equation is provided below, 2x+1x+1y''+2xy'-2y=2x+12 And one of its solution is…

Q: 0 1 0 0 0 1 -12 8 1 The general solution of x' = x is: 1 (a) x = Cje-3t -3 |+ Cze* 2 + C3e-2t -2 9.…

A:

Q: 6. What is the general solution of * (x2 + 2xy – 4 y)dx – (x? – 8xy – 4y²)dy= 0 x2 – 4y? = c(x – y)…

A:

Q: Suppose the equation y"+p(t)y'+q(t)y = f(t) is non-homogenous, has a particular solution y(t) et2,…

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Q: c. y' + 2y = x³ with y(1) = 2 Yo (x) = e Yp (x) = y (x) = y (x) = -2x 1½ e ²x³ - 2/ ( 10²x² -…

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Q: 1 2 9. A fundamental set of solutions of x': -3 -1 3 x is: 3 2 -2

A: We are entitled to solve only one question, so we will answer only the first question. Please post…

Q: Find the general solution of the following: x²y" + xy' + (x² – 49)y = 0 4y" - 4y - Зу%3 0 %3D

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Q: Are y₁ (1) = x, y₂(x) = ze² a fundamental set of solution for the equation r²y" − x(x + 2)y' + (x +…

A: Given thatand  are two solutions of DE

Q: 14. If f(z) = 2 + ² -r', then the equation S(z) = 0has a solution on the interval A [1,2] B (0,1] c…

A: Given equation, fx=2+x2-x3, To find the interval on which the equation fx=0 has a solution.

Q: Show by direct substitution that (-1)"+1 y = n-1 is a particular solution to (x + 1)y" +y' = 0

A:

Q: 10. A fundamental set of solutions of x' = 3

A: Given,        x'=-21-13-343-12x

Q: 9. The general solution of x' = -6 -4 x is: 2 | ++(-:)| (a) x = Cịe-2t + Cze¬2t (b) x = Cye" () +…

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Q: s of stick t

A: Given that it needs 5meters of stick to make a picture frame.

Q: 6. (E) Prove that there are no solutions to the equation 2x² + 5y² = 32² in positive integers (x, y,…

A: Given equation is    2x2+5y2=3z2  ------ (1)  Let's suppose that we have a solution x,y,z where…

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

A:

Q: 20. In question number 19, what is its particular solution? " (D² – D - 2)y = 1– 2a – 9e- Yp = 3e- +…

A: We need to find the particular solution of D2-D-2y=1-2x-9e-x Now, the particular solution is:…

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

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Q: 3 6. Let A = -4 Find the general solution of x' Ах.

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Q: y" + 3y' + 2y = 12x²; y(0) = a, y'(0) = b

A: Follow the steps below.

Q: Verify that yp, =3e²x and yp₂ = x² + 3x are, respectively, particular solutions of y" - 6y' + 5y =…

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Q: A fundamental set of solutions of x' = 3 2 x is: 1 (w) x. - “(;). x-() (F). (1). *--(;) (a) x1 = et…

A:

Q: 1 9. A fundamental set of solutions of x' = | -3 -1 3 x is: 3 2 -2 2 (a) x1 = e-2#| -3 , x2 = e-t X3…

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Q: What is the particular solution of y'=x²-2x+3,ify=4whenx=0? (A) B y=x²-x²+3x+4 3y=x²-3x²+9x+12…

A:

Q: 6. {y₁(x) = x, y₂(x) = x²} is a fundamental set of solutions of the reduced equation of x²y" - 2xy +…

A: Given that y1x=x , y2x=x2 is a fundemental set of solutions of the reduced equation of…

Q: Find the particular solution : y" – 2y' - 3y = 2e-t +3 (a) Yp =e-t +3 (b) Yp = -te-t 1 =-tet -1 (d)…

A: Particular solution

Q: 3 5 1 -1 a) x(1) = q (₁²¹) e² a (1¹) e ² + c₂ (₁) ₁² b) x(t)=q| 11) e ²² + 0₂ (1) ₁1e ²1 c) x(1) = q…

A: We have to find the general solution.

Q: Consider the problem of finding the number of integral solutions of the equation ₁+X2+X3+ *4 = 20…

A: (a) The equation can be rewritten as follows by adding the variables  y₁ = x₁ - 3, y₂ = x₂ - 1, y₃ =…

Q: j(x) = (2)(x – 7)3/2 + 1 EVALUATE                                              SOLVE j(11) =

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Q: etermine the equation of your model that will pass 2,4

A: We already have the equation of polynomialand

Q: This is the solution of y" + 4y' + 3y = 8 (t – 2) , y (0) = 0, y' (0) = 0 O y = [e-t-2) –e-8(t-2)] U…

A: