Use the method of variation of parameters to solve the initial value problem x' = Ax+ f(t), x(a)= x, using the following values. -el+5e³t 5e-5e³t 5e-¹-e³t A = 4-5 1-2 f(t) = 12 36 0) = 0

Q: (a)((x+1)² – y²)ª– (2(x+1)y – 10(x+1)²) = 0 dx

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Q: If y = a³ + e*, find y(4) when a = 0

A: Given: y=x3+ex   As we know that; The sum/difference rule: f±g'=f'±g' The Power law: ddxxn=nxn-1 And…

Q: Find an antiderivative F(x) of the function f(x) = - 2x²5x + 2 such that F(0) = - 15. F(x) = Now,…

A: On solving this we will get

Q: Use undetermined coefficients to find the particular solution to y'' - 3y' + 2y = e(-26-24x)

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Q: f(x)=x3-7x²+8x-3 iF Xo =5

A: Using Newton-Raphson Method we determine the approximation to the solution, where  f(x)=…

Q: please use the method of variation of parameters to determine the particular solution y'"+30y"…

A: The given differential equation is:y'''+30y''-4000y=e-20x

Q: f(x)= 3x2 -2, find f '(-2) O -12 none of these answers O 12 6x

A: Consider the function  f(x)=3x2−2

Q: If f(x)-3x+3x and f'(0)-3( by using 2-points formula with h=0.5), then the value of a is Select one:…

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

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Q: 2. Use the variation of parameters to solve: y" -2y" + y' = 4e*.

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Q: If f(x) = 18x2 + 96 3 ³√√x' find f'(8).

A: Given Function:- fx=18x23+96x3

Q: d’y - 2 y = 5x' + In(x²). dx

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Q: If f(x) = 16V1, then f"(4) is equal to 3/16 -1/2 6.

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Q: Given f(x)=-25sin (Sx) and f₁0) = -5 and f(0) = 4 Find F(1) 2

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Q: 1. Use the variation of parameters method to solve the equation y" + y = secx.

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Q: Find the value of the constants a and b given that F'(x)= 2ax + b, F(3)= 47, F(-2)= -3, and F(1)=3.

A: We have given F'x=2ax+b Then, integral on bothe sides we get ∫F'xdx=∫2ax+bdx Fx=ax2+bx+c where c is…

Q: 5. Given: f (x) = ax³ – 9x² + 2x – 4 and g(x) = bx³ – 5x² + 62x + 70 | Solve for all values of a and…

A: We have to find

Q: .1 Solve the equation x'y"-3xy'+3y 2x'e by method of variation of parameters.

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Q: Find the Derivative

A: The derivative of a function with respect to a variable is equal to the instantaneous rate of change…

Q: Given and f'(-1) = Find f'(x) = -5 and f(-1) = 0. = and find f(1) = = f"(x) = 5x + 1

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Q: (2) x (x+3)y"+2y'+y=0 solve for yox)

A: To solve the differential equation: x(x+3)y''+2y'+y=0 We can start by assuming a solution of the…

Q: h(x) = px³ + 4px + 1, where p and q are constants. Given that h(-1)=-41 and h'(-1)=67, find the…

A: h( x ) = px3 + 4px + qxh( -1 ) = -41 h'( -1 ) = 67

Q: Solve the DE using the method of variation of parameters: *y" 4ry' + 6y-6a, y(1) –3, y'(1) =2 All…

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Q: The general solution to the ODE x²y" + 2xy' - 2y = 0 is y = C1x + C2x-2. Use variation of parameters…

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Q: ii) Solve (x D²– 3xD+4) y = x² given that y(1) =1 and %3D - y'(1)= 0.

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