Show that: 2 2 4: +2} | sin 2y x=1 y=vx TOX dydx = 2y dydx+ _3 x=2_y=vX

Q: y +5y' +6y = 4e"+5 sinx

A: Given :-  y'' +5y' +6y = 4e-x +5sin x

Q: * Find dy/dx for the function y=2 sin(3x) cos2x 4 sin (3x) sin (2x) - 3 cos (2x) sin (2x) O 6 cos…

A: We know that derivatives  general power rule is - d(xn)/dx = nxn-1. And d(sinx)/dx = cosx ;…

Q: Show the solution of xdy/dx+2y=x^2 is y = x^4+C/4x^2

A: By arranging given differential equation we will get that it is of the form     y' + P(x)y = Q(x)…

Q: Find dy/dt and d^2y/dt^2 for function aln(y)+b cos^2(ty)=2t^3 where a  and b are certain constants.

A: Derivative two times simultaneously and use the forma for derivative

Q: if y = secx prove that y^2+y=2y^3

A: Equation relates the number of variables combined together by algebraic entities using equality…

Q: r10 xe -dx (x+2)(x+3)(x² – 1)

A: Using gaussian 5point quadrature

Q: if x(theta)=cos^3(theta) and y(theta)=sin^3(theta), how would we go about eliminating the parameter?

A: Given parameters Formula used

Q: The equation x''+ x = sin t has a bounded solution. true or false ?

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Q: 4(ax' + bx + e)]= (Sax + 3bx + c) d 1 dx 2x ,

A:

Q: 7. y = cos`x sin'x %3D 3 A. – 4 cos x sin x B. – 2 sin sin 2x 3 2 C.- 4 cos´x + sin' D.- 2 sinx cos…

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Q: The general solution for the equation y'=x*e(x^2+y) can be given in the form of: ?ex^2+2e-y=k a) x…

A: Solve by separable variable method

Q: What is the I.F of (2y^2+3x)dx+xydy=0?

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Q: I need to integrate 1/(sqrt(a^2+x^2)). If I let t=x+sqrt(x^2+a^2) where t>0, then how do I…

A: The given integral is,

Q: If 2x^4 + x^2y^2 - y^8 = 3x^2 + 4,what is the value of dyldx at point (4,1)? %3D

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Q: the

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Q: guess the form of the solutions 1- y’’ - 2y’ -3y = 3sin(5t)+tcos(5t)+2te^-t 2- y’’+2y+10y=4te^-t-…

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Q: y" = 2y^3 + 8y, where y = 2; y'= -8 when x = 4

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Q: dy + ydx %3D = 3x²y?dx,

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Q: solve for      xydy + 2(x^2 +2y^2)dy = 0 when x=0 and y=1

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Q: Find all solutions to the equation (D^2 − 3D + 2)y(x) = 2e^3x.

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Q: general

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Q: Which of the following equations can only be solved using parameter variation method? ay +9y sin…

A: Choose the correct options from below.(a) Let us consider the given differential equation, .The…