A characteristic equation has the following solutions: m,=7+2i, m2 =7-2i What is the general solution of the corresponding homogeneous linear equation with constant coefficients? O y = e7*(c,cos2x + Czsin2x) O y= e2X(c,cos7x+ C2sin7x) O y=C;cos(7 +21) + czsin(7 – 21) Ov=c(7+2i)e*+ c2(7 – 21)e* « Previous Next

Q: 23. Find the standard form of the equation. 81x -162x +36y² – 144y – 2691=0 (x-1)° , (v– 2)* - 1 [A]…

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Q: Use the substitution to solve the symmetric equation [Hint: We have x² + 1 x6 − 8x5 + 7x² +32x³ +7x²…

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Q: Prove that the equation ax + b = c has a unique solution where a, b, c constants and a≠0.

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Q: Q2. Determine all integer solutions (x, y), such that 0 ≤ a, y ≤ 100, to the following linear…

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Q: 4. Identify each of the given equations as linear or non-linear and homogenous or non- homogenous.…

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Q: Show that r =1+i, x2 = 1- i is a solution of (3+ i)x1 + (1+ i)x2 = 4 + 4i

A: The solution is given as

Q: Find the solution. (4D4 - 4D3 - 3D2 - 2D + 1)y = 0. A y = (c,+c,)e*+ (c,+cx)e/½ y= (c,+c)e/2+…

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Q: Find two linearly independent solutions of y" + 1xy = 0 of the form Y₁ = 1+ a3x³ + α6x6 +.. Y₂ = x +…

A: The given problem is to find the coefficients of the 2 linearly independent solutions for the given…

Q: Solve these equations using the given substitution: 1) y' + 3y + y² = 0 1 with z=- y

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Q: Show that the equation 24 = (-5 – i/T) z+(60 – 80 i) has no solutions in the closed disc z| < 3.

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Q: Show that ri =1+i, r2 = 1-i is a solution of (3+ i)x + (1+ i)x2 = 4 +4i %3D

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Q: Cartesian equation of z+1=3 is o (x + 1)2 + y2 = 9 o(x-1)2 +y2 9 ox? + (v + 1)² = 9 o(x+1)2-y2 = 9

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Q: Solve the Euler- Cauchy equation

A: We solve the given differential equation using Euler cauchy method.

Q: (b) Show that general solution of the second-order difference equation: yk+2 - Gyk+1 + 8yr = 2+ 3.k²…

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Q: solve for w,x,y,z using Gaussian elimination

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Q: 18. Find the standard form of the equation. 36x + 288x+64y² -768y +576= 0 (x-6)° ¸ (v+4)² _ [A] 1 36…

A: Given equation

Q: x +y + 2z=1 2x-y-z = 0 x +2y-z = 4

A: Follow the steps below.

Q: 8. Linear Equation of Order 1: Solve the equation (2x + 3) y' = y + (2r + 3)i; when x = -1, y = 0

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Q: Use the variation of parameters formulas to find a general solution of the system -3 2 et y' 2 -3 2…

A: The method of solving a nonhomogeneous linear system of differential equations is the following.

Q: find all the values of a such that y=xa is a solution of yII-12x-2y=0

A: The objective of the question is to find the values of 'a' for which the function y = x^a is a…

Q: Show that a riccati equation with constant coefficients y'+ ay² + by + c = 0 has a solution of the…

A: To show that  a riccati equation with constant coefficients y'+ ay² + by + c = 0 has a solution of…

Q: Find two linearly independent solutions of 2x²y" - xy + (-4x + 1)y=0, x > 0 of the form y₁ = x¹(1+…

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Q: Find two linearly independent solutions of y" + 3ry = 0 of the form Y1 = 1+ a3x³ + a6x® + · .. Y2 =…

A: We find two linearly independent solutions of the given differential equation  y"+3xy=0.......(1)

Q: 1 y" +y+y=x²-2x 4

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Q: Select all equations that are equivalent to a-6z 16. a + 6x 9 0 O b a + 6x +9 = 16 Oc a+6x + 9 = 25…

A: Solution:-Given equation,     x2+6x=16  —1let us see and solve each option given,a…

Q: Which of the following equations can be rearranged into separable equations? Select one: а. (х + у)у…

A: (a) (x+y)y'=x-ydydx=x-yx+y Now it is difficult to separate.   (b) y'=x+y2x2+y+1dydx=x+y2x2+y+1Not…

Q: Solve the Cauchy euler equation d²y + 6x 2-6y = 3 + Inx3 dx x3 d3y 3x2 dx2 dy dx3

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Q: Solve the following equations system 0.17 – j0.2V, =1 - j0.2V, +(0.2+ j0.3)V, = j0.5 V,= 3.3333 +…

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.