Problems: Find the general solution 1- y" +2y' + y = 4e* In x

Q: If y = u³ - 4 and u = 3x² + 10, find y' O 18x(3x² +10)² O 3x(6x² + 10)² O18(3x² +10)² 6x(3x² +10)² घ

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Q: When the height of the sand in a particular rectangular sandbox is leveled out then the height of…

A: The height of the sand box is proportional to the volume of the sand. When the height is 2.25 in the…

Q: Example 4: Solve iv) y" – 2y' + y = 3e2x.

A: Given differential equation is, y"-2y'+y=3e2x The auxiliary equation of this differential equation…

Q: Consider that Let the solution of equation y₁ = x² y2 = 3x² - y3 = 4x-2 2 x² x²y" + xy' 4y = 0…

A: All the parts are solved properly with detailed explanation.Hope you got your answer. If any query…

Q: Solve Ux + X YUy +U=0

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Q: Solve the given DE x?dy - xydx-2ydx

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Q: would you prove that the answers to the diophantine equation y^2-x^3=0 are the pairs (n^2,n^3) for…

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Q: Solve (x² + 4)y' = 2xy In|x] = In(y? + 4) +C O Option 1 Inlyl = In(x² + 4) +C

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Q: 1.) y(4) + 4y" + 6y" + 4y' + y = x³e=x

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Q: y" - 5y' + 6y = 0

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

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Q: Problem 2 Solve y" - 25 y = x ex

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Q: Find two fundamental solutions x²y" + 4xy' + (2+x)y= 0,

A: We have to solve given problem:

Q: If the general solution of (2+²-3y2) y'= 2xyżsy"In|y"+xª = Cy", what is the value of b? (A) 3 B 2 -1…

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Q: Example 4: Solve i) у" - 2у' + у 3 Зсохх + 2sinx.

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Q: 2x Example: Show y = ae¯* +be* is a solution of = de y"-y'-2y 0 for all values of a and b. %3D

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

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Q: 7. Given 2x2y" + xy' + 3y = 0 show that 2x2y+2) + (4n + 1)xy"+1) + (2n² – n+ 3)ym) = 0 %3D

A: We use the method of mathematical induction to show the given statement holds (given…

Q: 4. Find the general solution to the DE 2x²y + xy'-3y=0.given that y₁=- is solution.

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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: 2. y" - 3y' +2y = e4x + 6x³ – 2+ 3sin(4x) | |

A: See 2nd step

Q: 1 Q6 Solve y" + 3y + 2y = 1² 1+e

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Q: b\ Find the domain of the functions: (1) y = (2) y = = (3)f(x) =

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Q: Solve

A: Topic:- solution of differential equations

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: (1) y "'+ y "– 2y = 3+2cosx

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Q: y-y"+y'- y = xe* -e-x + 7

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Q: The particular solution (yp) of the equation y" - 3y + 2y = 5 e* is yp = -5xe*

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Q: e general solution to y" - y' + (81x¹ −72) y = 0. X

A: Given    y''-5xy'+81x4-72x2y=0  Here we use the formulas:  to find Integrating Factor(I.F)=e∫P(x)dx…

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

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Q: Find the general solution to the homogenous DE y'-16у' + 64у %3 0

A: The given homogeneous DE is y''-16y'+64y=0. The auxiliary equation is m2-16m+64=0.

Q: Find the general solution to x^2y'' + 4xy' - 10y = 0

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Q: Can you substitute equation 28 into equation 27 and try to achieve equation 30? Please I need it…

A: We will use the basic knowledge of substitution techniques to answer this question properly, in…

Q: M 3. Solve by using undetermined method Coefficients y" - Sy' + by = xe X of

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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.