determine the function f(x)=C_1e^(-x)cos(x) + C_2e^(-x)sin(x) is a solution of the D.E. y"+2y'+2y=0

Q: 1 -dx = /8-(2x+5)² o įsin- (2*) 2x+5 + c V8 2x+5 sin-1 + c 8, tan- ( V8 2x+5 + c o ţtan" (2*5 ) + c…

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Q: Solve the Bessel equation x^2y''+2xy'+(x^2-4)y=0

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Q: Find f'(x) where f(x) 32 x cos (x).

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Q: Find f'(x) if f (x) = 2 cos x + 3 sin x. f'(x) =

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Q: Find the second derivative of f(x) = x2+ e* - COSX. O a. f(x) = 2x + xex - cosx O b. f'(x) = 2x + e*…

A: Solve by derivative

Q: Set up the appropriate form of a particular solution yp of the dif- ferential equation…

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A: Solution to find the derivative for the given function is as follow .

Q: Show that the solution of the differential equation dy/dx=sin(x+y)+cos(x+y) is  1+tan(x+y)/ 2 =…

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Q: Given f'(x) = 6 cos x - 10 sinx and f(0) = -5, O find f(x) C

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Q: Get the first order derivative of the function x + sin(y – 2x) - 1= 0 - 2 1 a. y' = cos(y-2x) 1 b.…

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Q: Find f'(x) if f (x) = 3 cos x + 8 sin x. f'(x) =

A: We need to differentiate the given Function.

Q: Find f, f "' (x) = cos(x), f(0) = 4, f'(0) = 4 f'(0) = 9 f(x) =

A: Given: f'''x=cosx, f0=4, f'0=4 and f"0=9 To find: fx Solution: We have f'''x=cosx Integrating both…

Q: Let f'(z)= 8cosx-7sind 2 f'() = 0 f(x) = 8 sin x + 7 cos x

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Q: Find y\\ for each of the following functions: 1- f(x)=sin(xe). 2- f(y) = sin (3y)+ e-2y + In (7y)

A: d(u v) = u dv +v du

Q: Find the solution. (403+12D²+13D+10)y = 0. @ y=c,e+e>(c,cosx + c sinx) +c,sinx) -3x y =…

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Q: Find f'(x) = = 4-5 sin(x) cos²(x) f(x) = -4 sin(x) + 5 cos(x)

A: Given : f(x)=-4sin(x)+5cos(x)   To Find : f'(x)

Q: Given f’(x)= 3 cos x - 9 sin x and f(0)= -6 find f(x)

A: We can solve this as follows:

Q: Solve (e' +1) cos x dx +e'sinxdy = 0

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Q: Obtain the particular solution of \frac{dy}{dx}=\frac{1+ycosxy}{3-2y-xcosxy}.

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Q: h'(x) = cosxcot(sin^3x)+cosxsinx ⠀ h(x) = sin(x) -2 (cos(t³) + t)dt

A: Applying Leibniz's rule

Q: If f(z) = cosz - 3 tanz, then f'(z) = -sin(x) - 3 sec²(x) f'(2) =

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Q: If f(x)=√x+3, g(x)=x², then (fog)(x) = The differential of the function f(x)=tan(cos.x) is_ The…

A: We know that derivative of d(cosx)/dx = -sinx. And d(tanx)/dx = sec2x. And derivatives power rule is…

Q: y for the function f(x)= cos [x*sin (x²+1)] =, CoS 1/2 %3D ..…

A: The given function is fx=cos3x3sin12x2+1. Obtain the derivative as follows.