2. Verify that r = Cie +C2 is a solution to a" – r' = 0. Find C1 and C2 so that r satisfies x(0) = 1 and a'(0) = 10.

Q: Eliminate the constant: 2x 3x =c₂₁e²x + c₁₂e³x Oy"-y'-6y=0 Oy"-5y'+6y=0 Oy"+y'-6y=0 Oy"+ 5y'+6y=0

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Q: find the seril solution of the equation y``+  4xy = 0  at the neighborhood of the  point  x0 = 0

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Q: Find the real valued general solution of y" + 5y = 0. %3D

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Q: Verify whether yı = 3t4 and y2 = 4 t-2 form a fundamental set of solutions for f y" +7t y' + 8 y =…

A: We will verify the given statement.

Q: Verify whether y(x) = 2e-*+xe-* is a solution of y" + 2y + y = 0.

A: Topic = Differential equation

Q: 5. Use the method of variation of parameters to find the general solution to _y"—y'—2y=e³x.

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Q: 2) x + xy+y -7= 0, (1,2) Ans. -4/5

A: We have, X^2 + xy + y^2 - 7 = 0 Differentiate with respect to x, we get 2x + [ x • dy/dx + y • dx/dx…

Q: Solve by reduction of order. Find y2 and y (x² + 1)y" – 2xy' + 2y = 0 yı = x -

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Q: Use variation of parameters to find a particular solution of y" - y =

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Q: x' +(log3 3)x – v2 = 0

A: Note: If a polynomial gives one solution in complex number then conjugate of this solution must be…

Q: where y1 = e* is one of the functions in the fundamental solution set. - %3D xy" + (2-2x)y' +(x- 2)y…

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Q: ye x, (21x) satisfie s Show that the equation

A: Given: The given equation is xy''+n+1y'+y=0  ,  y=xn22x

Q: 9. y" +9y = 0

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Q: Are the functions y₁(x) = e, y2(x) = ze a fundamental set of solutions for the equation y" - 2y + y…

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Q: Determine (without solving the problem) an interval in which the solution of (9-1²)y + 2ty = 4t²,…

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Q: Find the general solution of y" = x-1 A. y = xln x – C1x + C2 B.y = xln x – C1x - C2 C.y = xln x +…

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Q: x²y" – 5xy'+9y = 2x

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Q: DETERMINE SOLUTION OF 1 x dy dx + y = x² + x (2x+3y-13) dx + 3x - 2y) dy = 0 DE

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Q: Given y1 = Vi a solution of 4t²y" +y= 0. Find a second independent solution.

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Q: Show that the y = √x/₁/4(kx²/2) is a solution of y" + k²x²y=0_

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Q: Find the general solution to 3x y" + 9y= e³x + secx.

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Q: Suppose that x-y" + axy' + by = 0 has the general solution of the following form: y = C,x³ + C2x³ In…

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Q: =² + 2y²) = ry, y(-1) = 1 dy O 2n* = y² + a? O a* = 4 (y² + a²) O a4 = 2 (y² + x²)

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Q: 8. Solve the Cauchy-Euler equation 4x²y" + 8xy' + y = 0.

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Q: 3 ť'y" +7t y' +1o yoo

A: A detailed solution is given below

Q: 7. Verify that y = x2 - 1 is a solution of (y')* + y? = -1.

A: Given- y=x2-1 To verify- That the above function is the solution of y'4+y2=-1.

Q: 5. The function y₁=+1 is a solution of (1-2-2³)+2(1+)/-2yy=0. Find the general solution.

A: PLEASE NOTE: There is a slight  typing mistake in this question ,the differential equation should be…

Q: Solve the IVP: X' = AX, where -() xw - () 3 -3 1 A = 2 -1 0 1 -1 1 and 7 X(0) 4 3

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Q: 1. If x²y-xy² + x² + y² = 0 find y'.

A: NOTE: As per our guidelines, I have solved the first problem. If u want the answer of other, kindly…

Q: If C = 3x + 6 x [³y + 4z 2+²]·D= [32¹] and C = ,D -y z+

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Q: Determine three linearly independent solutions to the equation y" + 2y" – 3y = 0 of the form y(x) =…

A: The given differential equation is                                                y'''+2y''-3y'=0

Q: Find a general solution to (ax+b)y"+a(ax+b)y'- y3(ax+b)°, where a,b >0 with ax +b >0 for all x on a…

A: Given equation is  ax+b2y"+aax+by'-a2b2y=ax+b1b Cauchy Euler equation . To solve this put…

Q: What is the solution to y' +2 = xy3? * +c a. b. = -x +c c. xy? = - +c d. xy = -x² + c e. None of the…

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Q: 1. Verify x₁ = t²x² = (' -3t 5 3t+²) and x2 = 5t 3t² -2t X. t -t-> - are solutions to

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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.