5 || I2 = Solve the following initial value problem: 5 -4 d ² = (₁ = 3 ) * dt 4 - + 18e³t 12 z (0) = ( ¹² ) 36t ), Z(0) = 5

Q: 20.12 Solve 6 d²u 8x² - d²u 5- d²u + oxdy dy² = 14, subject to u = 2x + 1 and du/dy = 4-6x, both on…

A: The given partial differential equation is       6∂2u/∂x2 - 5∂2u/∂x∂y + ∂2u/∂y2 = 14. So,…

Q: Given the function y = x3 + x² + x + 10, suppose x increases from 1 to 1.1. Find the absolute error…

A: We will find out the required value of absolute and percentage error.

Q: Solve the following : dy _ 4x+6y+5 (i) dx 2x+3y+4 dy dx (ü) x- +y = y² log :

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Q: 1. (2+ y'y' dy 2. [(1+x)? Vxdx

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Q: Find the general solution to the following equations (4 -2 x'(t) = X. 8 -4

A: The solution is given as

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: -3/2 -¹² (2²³ + 2x) da with y(0) = 0, y(3/2) = 1. (c) J[y] = =

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Q: In the equation y = a ln (lambda x) + b, how can I isolate (1) a, and (2) the lambda?

A: Simple parametre reduce problem......

Q: valuate the following: a. L {e3t + cos6t - e3t cos6t} b. L-1 {6s/(s2 + 25) + 3/(s2 + 25)} c. L-1…

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Q: Solve the following equation y" + 2/ + y = * using the method of variation of parameters.

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Q: 20. g(n) = (3x – 2)(4x' + 1) 22. f(1) = cot (2r) 24. S(x)=

A: solution is given below

Q: Given y' = 4x x²+2 A. 4x ln x² + 2 + c B. C. D. find y. 4ln|x² + 2] + c 2x ln |x² +2|+c 21n|x² + 2]…

A: We will use integral to find y from y' , using y'=dydx

Q: y'' = 2y' - 5y         y(0)=pi, y'(pi/4)=0

A:

Q: SOLVE STEP BY STEP IN DIGITAL FORMAT 3.16 Use variation of parameters to obtain a particular…

A: Given differential equation  we have to find particular solution by variation of parameters.

Q: 5. (y – x + 3)dx + (x + y + 3)dy = 0; x = 1; y = 4. Solve in two different methods.

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Q: Use variation of parameters to solve the same ODE in the previous problem y" - 9y = 4e³1

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Q: Apply the method of reduction of order (not itť's formula) to find the second solution if 6y"+ y'-y…

A: Write the given differential equation 6y''+y'-y=0 in standard form by dividing by 6 throughout.…

Q: y(4) - 4y" + 6y" - 4y+y=0; y(0) = 0, y'(0) = 1, y'(0) = 0, y" (0) = 1

A: The Laplace transform is used to find the solution of the linear ordinary differential equation with…

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: Q/Solve the following initial - Value Problem: хе x ex³dx + (x³²-1) dy=0

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

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Q: Compute the quadratic form 1/3 x'Ax, when A = 1/3 [s 5 and X1 а. х%3D X2 -[:] b. х%3 c. x= 3

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Q: 2ty t²+1 – 2t – (2 – In(t² + 1))y'

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Q: 4. Find the (real-valued) general solution of x' = 2 0 0 0.0 31 -4 3 X.

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Q: 6. Solve the IVP with y(1) = 2 and ty' = 4t² - 2y.

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Q: Solve the following IVP y' = e- (2x - 4) dr de == y(5) = 0 r(1) = 2

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Q: (3) y "'- 2y "– 4y '+8y = 6xe²* %3D

A: Note: " As per our guidelines we will solve only first question . If you want any specific question…

Q: •1 1 g(x) = dt 2x In(t + 1)

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Q: e + xy + 4x = 1 ise y"(0) =?

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Q: (19) ds dt t= -1 if 5=1-3t

A: The given function is s=1-3t2

Q: Solve the following 2nd order D.E using variation of parameters method: y'' + 2 y' + y = e^(-x)

A: The non homogeneous differential equation is given as y''+2y'+y=e-x Corresponding homogeneous…

Q: (11) 10y" - 3y' – y = 0

A: Explanation and solutions is given below....

Q: 7. Find the first derivatives of each of the following: 'a. y= 10x – 4x² + 6x – 12 b. g(x) = x'e* c.…

A: we have to find the first derivative of the following: (d) ft=4t3sect (e) log65x+13

Q: j(x) = (2)(x – 7)3/2 + 1 EVALUATE                                              SOLVE j(11) =

A: