Consider the initial value problem 0 ÿ' = = [2²2 ÿ+ģ(t), 4t 2t² -1 Suppose we know that 0 = - [2] -2 ÿ(1) =

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: Find a general solution to the following higher-order equations. (a) y'' - 5y'' +6y' +12y=0 (b)…

A: The given differential equations, a) y'''-5y''+6y'+12y=0 b) y'''+3y''+y'-5y=0 c) y'v+13y''+36y=0 We…

Q: (B) Find the general solution of x²y" - (2a-1)xy' + a²y = x²+¹ where a is a constant. Good Luck

A: This question is about ordinary differential equation.

Q: 15. Let 2 √x 4 3/2 y' = 2y + 2xy' 13/2 Solve for y' when x = 1 and y = 4

A: NOTE: Refresh your page if you can't see any equations. . here we have x=1 and y=4

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: Example 2: Find the particular solution of (x – y)dx + (3x+y)dy = 0 when x = 2 & y = -1.

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Q: Solve the following IVP: X' = AX + f(t), where 2 -1 A = 3 -2 and X(0) = ( : -3 2 f(t) 10t ||

A: First we need to find the eigenvalues and eigenvectors of a then find the complementary solution of…

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: 2x y" +5xy' + y = 3x +2 Answer y(x) = +은+2+

A: The given equation is of the form ax2y''+bxy'+cy=g(x) The solution to the above equation is given by…

Q: Find the general solution of (1+ x²)y' + xy = x=1(1 +x²)-/½

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Q: 8.) y" +2y' +5y = 3e 2* ; and y(0) = y'(0) = 1

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Q: Find the general solution of y""- 5y"- 6y'=0

A: The given differential equation y'''-5y''-6y'=0

Q: (a) Solve y" + xy + (2r – 1)y = 0, %3D near z = -1, if y(-1) = 2; y'(-1) = -2.

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Q: 5. Solve 3y" (x) + 2y'(x) - 8y(x) = 0, y(0) = 6, y'(0) = 18

A: 3y''x+2y'x-8yx=0y0=6y'0=18

Q: (h) xy" + 8y' +18xy = 0, xo = 1 (i) (3 — x²)y" — 8xy' - 18y = 0, xo = 0 (j) 2y" + 8xy' + 18y = 0, xo…

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Q: Use undetermined coefficients to find the particular solution to y'' + 2y' – 4y = 2t + 2 Yp(t) =

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Q: Find the general solution of EonC(2)'y/n-1),

A: ∑i=0nnCi(2)iy(n-i)

Q: x²y"-9y" + 6y' - 9 = x² + 6x y'(0) = 0

A:

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: dy %3D 1. If x'+ xy-3y' 10, then dx %3D

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Q: 1) Find the general solution of the equation x³y" - 2x²y" - 4xy' + 8y = x² + Inx.

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Q: 3. 2хydx - (3xу + 2y?)dy %3D0 o (x - 2y)*(2x +y) = c O (x - y)*(x + y) = c (х + 2y)(2x - у)*- с о…

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Q: Solve the initial value problem x2(dy/dx)=(3x2-x-5)/(x+1)(y+1), y(1)=2

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Q: X -is If y = x² — xy + 1, then when a = 1, d - 0-1/1/12 01/22 0-1 0-2 O nonexistent

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Q: Solve the given differnetial equation by undetermiend coefficents  y'' + 2y' = 2x +7 -e-2x   y(x)…

A: Given:-           The differential equation  is:…

Q: - Sapotri to solve 2x?y" – my + (x + 1)y = 0. n=0 12) Use y =

A: Given: 2x2y''-xy'+x+1y=0. To Do: Solve the given differential equation using y=∑n=0∞anxn+r.

Q: Solve y'+by+9y = 0, y(0) = −2, y'(0) = 7 y(t) =

A: Given :

Q: Find a third degree polynomial which approximates the solution to the initial va problemy" + 2xy -xy…

A: The given differential equationLets solve it using the Taylors polynomial

Q: y' 3x² + 4x - 4 2y-4 y (1) = 3

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Q: Solve (D-2)²(D²+1) y=0,y (0)=1y '(0)=2, y'' (0)=3, y''' (0)=4

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

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Q: 3. Find the general solution of the following DE. y' = 3 (y + 1) O y = ce³x - 1 3y = ce³x - 1 Oy =…

A: Use variable separable to Solve this problem.

Q: 2. Solve the initial value problem: 2 + 2y = 6e¬*;y(0) = 8 %3| dx

A: To solve given initial value problem first we solve for integrating factor for given first order…