1 1 التاريخ : Q: find the solution of This system of ordinar equations by numerical Euler's method _ 2 Y₁ (t) = y₁ (t) —2 Y₁₂ (t) + 4 cos (t)- 2 sin (t) » X₁ (0) == 3 Y, (t) - YY/₂Ct) + 5 cos (t) - 5 sin(t) 1₂ (0)= Yz (t) 1 9

Q: 1. y" - 3y' - 10y = -3

A: We need to solve the differential equation.NOTE- As per Bartleby guidelines we can solve one…

Q: Consider the Riccatti equation Please answer all parts. v'=v2-(7/x)v+8/x2 a) use the substitution…

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Q: Find the general solution of the following equations (The answer can be given either explicitly or…

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Q: Find the solution of y" − 8y' + 16y = 0, y(0) = 1 and y'(0) = 5. y(t) = Ae4t + Be-4t y(t) = e4t+te4t…

A: The given equation is;  y''-8y'+16y=0, y(0)=1 and y'(0)=5. We have to find the solution of given…

Q: Find the general solution of (D²-7DD' + 12D'2)Z = sin(x - 2y) + ex-2y

A: This question is from linear partial differential equation.

Q: Find the solution of x²y" +5xy' +(4+4x)y=0, x > 0 of the form n =1,2,3,... where co 1. Enter r = =…

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Q: What is the general solution of the given equation, cos(x + y) + 2x + (cos(x + y) + 4y)y' = 0 OA…

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Q: If do, a1, a2, A3, ... is a sequence of increasing real numbers, then for large enough j it is the…

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Q: Consider the equation ut = Uxx, 0 0. Suppose u(0, t) = 0, u(1, t) = 0. Suppose u(x, 0) = -3 sin(x) +…

A: The given equation is  ut=uxx ,0<x<1,t>0. Boundary Condition: u(0,t)=u(1,t)=0. Also…

Q: Find the fundamental solutions and write the form of the particular solutions. No need to find the…

A: Here we have to find the fundamental solutions of the given differential equations and write the…

Q: The equation y" + y' +cos (t) y = e" (9 – t) can be solved by O a) Undetermined coefficients O b)…

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Q: Question 10 152 0 0 1 Describe all solutions of Ax = 0 in parametric vector form, where A = 0 0 0 0…

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: 000 SUD 31 (i) y" +4y= 2 cos²x+10e

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Q: Solve the problem p"+x=0, p(0) = 1, p'(3)=0 with two linear elements of lengths 1 and 2…

A: The problem seems to be a second order ordinary differential equation (ODE) with the form p'' + x =…

Q: Q4) Solve the following nonlinear system : cos(3x) + cos(y) = 0 cos (5x) + sin(y) = 0 where %3D %3D

A: 4. The given equations are,cos3x+cosy=0cos5x+siny=0with the initial condition x0y0=-21

Q: Write the system y1 = -y1+2 cos(r)y3 + e 2 = xy1 - 10y2 + e" y3 +20 sin(x) Y3 = e2" y2 – a²y3 %3D…

A: The matrix form of given system of differential equations as follows

Q: The general solution of (D²+2D +1)(D²+4)y=0 is A y=(C,+Cx)e+C,cos2r + C ,sin2r B…

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Q: y" − 4y' + 4y = 0. Find two solutions. Show that the two solutions in part (a) form a fundamental…

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Q: Given equation y'''-2y''+2y'=0 A) find the auxillary equation and its roots B) Find the general…

A: a.) The auxiliary equation is:m3−2m2+2m=0The roots are:m={0,1+i,1−i} b.) The general solution…

Q: Using variation of parameters, solve the nonhomogeneous system X'= AX + g, where 1 A=[24] g=g(t) =…

A: Given that the nonhomogeneous system                      X'=AX+g, where                A=21-5-2,…

Q: Solve the he o-3D+4)y(x) =x cos(2x) equation y,(x)=(6x+4)sin( *+4)sin(2)-cos(23) - y,(x) =(-6x-4)…

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Q: Find the fundamental set of Frobenius solutions 0 x²y" -x(5-x) y' + (9-4x)y = 0. Give explicit…

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Q: e) y-2y'+y

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Q: -4 Find the general solution to the second order system x' " х+ -5 cos(2t). 2

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Q: Q6. Use the method of Variation of parameters to solve (i) y" + y = tan x. (ii) x²y"+xy'+(x² – })y =…

A: Hint: particular solution of a differential equation from method of variation of parameters suppose…

Q: ニ

A: The given differential equation is y''+2y'+y=2e-x1-xsin 3xy''+2y'+y=2e-x-2xe-xsin 3xHere the…

Q: A swimming pool has volume of 1,500 m³ and has a length of 18 m and a width of 14 m. Determine the…

A: We Know that  Volume of a cuboid = length × width × height(depth)  Given  Volume of swimming pool =…

Q: 5. It is given that two linearly independent solutions of x²y + xy + - y=0, x>0 are -1/2 sina and…

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Q: Solve the equations in Exercises 1-16 by the method of undetermined coefficients. 1. y" 3y - 10y =…

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

Q: Q4(a) (b) Find the complete solution of p? +q2 =z, where p = ax Find the general solution of d²q dq…

A: This is a problem of the differential equation.

Q: لام ( = = 3 e + 2 = 1 * " - 49 + 2 +49 - ax له +2 ه = 4 + 4 + 4 - 2 4 = (0) و ر ۱ = (0) × 1 = (Xo…

A: We'll answer the first question since the exact one wasn't specified. Please submit a new question…

Q: The system x' = cos(t)x+ sin(t)y y' = cos(t)x - sin(t)y is linear.

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Q: Use the method of Frobenius to solve the given equations. a) 2x?y" – xy' + (x² + 1)y = 0 b) 2x?y" +…

A: Since the solutions of the given equations are very lengthy in Frobenius Method , i gave the…

Q: 2. Determine whether sin x or cos x is a solution to y" - 2(cot x)y' + (1+2 cot² x) y = 0 Hence use…

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Q: *у +2ху - 6у - 0

A: General solution of cauchy euler equation x2y"+2xy'-6y=0