Iff(x) = −4x2 + 7x + kandf(0) = −4,find k.

Q: Find the particular solution for y' = x3 – 2xy when x = 0, y = 1

A: We are given a differential equation: dydx=x3-2xywith the initial cobdition x=0, y=1 We can solve…

Q: 3) Evolvate Ci(0) e²/z dz е

A:

Q: (D² + D)y =x+| ;

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Q: Solve the particular solution (D2+3D+5)y = 5e-xsin2x using  D- operator method.

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Q: find the general solution. 6y'' - y' - y = 0

A: Given differential equation ,6y''-y'-y=0

Q: Solve by the subtitution method  x=3y+10 x-2y=13 (x,y)=

A:

Q: find general solution. dr/dt= -2tr,         r(0)=ro

A:

Q: Find the general solution of (T^2 + 4)y' + 2ty = t^2 (t^2 + 4) with the variation of parameters…

A: In this question, we find the general solution of (t2+4)y'+2ty=t2(t2+4) with the variation of…

Q: Find the general and particular solution of the y"=3e³x if f(2)= k and f'(2)=k²

A: y"=3e³x if f(2)= k and f'(2)=k²

Q: What is the general solution of 3 (3z + y') dz – 2zydy = 0?

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Q: (1+ 2.x² þ" – 4.xy' + 4y=0 yı(x) = x

A:

Q: Find the general solution using variation of parameters. y" – 4y + 4y = (x + 1)e²"

A: Given differential equation is, y"-4y'+4y=x+1e2x The auxiliary equation is, m2-4m+4=0m-22=0m=2,2…

Q: Find the general solution of (D3-D2+D-1)y = 15sin2x using method of undetermined coefficient.

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Q: Find the General Solution: y" - 3y' + 2y =e*

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Q: What is the solution of y2 - x2y'=0 with IVP y(1)=1/2 ?

A:

Q: Find the particular solution of y''-5y'=x-2 when x=0, y=0, y'=2

A: Given that that a non homogeneous differential equation and we find its solution.   Here i attached…

Q: Q2. Solve the DE. y"" = x2sinx 1. by using inverse operator method. 2. by using variation of…

A: As per bartleby guidelines for more than one questions asked, only one questions is to be answered,…

Q: 2xyy' 1+ y2 What is the general solution?

A: The solution is given as

Q: 2senx y' - 2y =

A:

Q: Solve for Z. X= (Y-Z) 3

A: Given: X=23Y-Z We have to solve for Z.

Q: What is the particular solution for y′=6ex+7x3−7x+1 such that y(0)=−4?

A:

Q: Use Variation of Parameters to obtain the General Solution 1. y +4y 4-sx2x

A: Solve the given problem.

Q: Solve using the chain rule f(x) = 6/2x – 5 12 A. 6V2x- 5 В. 2х-5 6. C. 12x/2x –5 С. D. V2x-5 - O A O…

A:

Q: Find the general solution using variation of parameters. - 4y + 4y = (x + 1)e²-

A: To solve the following problem

Q: e²–3¤ /1 – y² given that wher

A: Given that, dy/dx = e^(2 - 3x) . sqrt (1 - y^2) Then we get, dy/[sqrt (1 - y^2)] = e^(2 - 3x) dx…

Q: What is the particular solution for y′=6e^x+7x^3−7x+1 y(0)=−4?

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Q: S: - V dx 2x - √x + 4 VX

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Q: y" – 6y' + 9y = :

A:

Q: Find the General and Particular solution of = 3y ; y = 3, when x = 0

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Q: Find the general solution Ans. y=(C1+C2x)eX+e*

A:

Q: y' = - 2xy

A: The given differential equation is y'=-2xy⇒dydx=-2xy The given differential equation can be solved…

Q: -solve the following system by using the method of undetermined coefficients. dx1/dt= 2x1-5x2-cost…

A:

Q: Qs) y" + 3y' + 2y = e* – 3

A: See the details solution in below

Q: e general solution of y6) + 4y(4) + 3y" = 0 ?

A:

Q: b. Solve y = -x³ + x² + x- 3 and y = x-3 using Substitution Method. I

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Q: 4. Solve for x. MZWYX = 56x +1 M2WLX = 58x - 1 4. Solve for x Y

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Q: What is the particular solution of 2xyy' = 1+y2 , when x =2, y = 3

A: The given differential equation is solved below in detail.

Q: 4. y = vx + 2 x,for-

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Q: (b) Solve y" + y = 0, y(0) = 3, y(1) = -3 by using finite-difference method with h = 0.2.

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Q: 2x³y' = y(y² + 3x²) using Bernoulli.

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Q: note that X - y +z = e2 and 4x – 3y + 2z = e2

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Q: Find 6 [2f(x) – g(x)]dx = i - if 6 6. = 2 and g(x)dx = 10

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Q: Y1 (x) = 8a + 2x; y2(x) = x In(bx); y3(x) = ca?.

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Q: 3. 2y" + у' %3 А. 3 В. Зx2 С. Зх D. x?

A:

Q: Calculate y(k)(0) for 0 ≤ k ≤ 5, where y = x4 + ax3 + bx2 + cx + d (with a, b, c, d the constants).

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Q: Use variation of parameters to find the general solution of y" – 2y' + 5y = e'.

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Q: Find the general solution of (2x –y) = 2y – x

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Q: Find General Solution of y" + y" = 0.

A: Given the differential equation is y"' + y" = 0. Here the auxiliary equation is m3 + m2  = 0

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.