X, Y, Z ~ beta (alpha=1, beta=2) => p(X < sqrt(YZ)) = ?

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: Find f'co) if fco)= (Since\ %3D

A:

Q: The integrating factor (IF) of the equation y' - 2ycot2x OA. sin2x OB. cot2x O C. Lnsin2x OD. CsC2x…

A: To find the integrating factor IF of the following equation,y'-2y cot2x=1-2x cot2x-2 csc2x

Q: y = 5t2 - 2t + 4 -'(t) =

A: The given function is y=t25t2-2t+4. We have to find the derivative of the given function. The…

Q: Use the table to determine D,f(g(x))) at x= 3. 3 4 f(x) 1 f(x) 3 -5 8(x) 2 g'(x) |1 4 3 2 4 1 3 6 -5…

A:

Q: TEST FOR HOMOGENEITY: */70 3. e"

A:

Q: Find y' of cot (xy2) + xy = x².

A: Given query is to find derivative of the expression.

Q: y = () Зx2-2 х+3

A: I am using the chain rule to find the first order derivative of the given equation

Q: 3. Why can you not use the power rule to differentiate y = e*?

A:

Q: 2- Solution of the following function {(dy/dx)-(cotx) y=(csc x)y³ }

A: The differential equation is given as dydx-(cot x)y = (csc x)y31y3dydx-1y2cot x = csc x…

Q: Find the point on the curve y = Vx +1 that is closest to the point (5,0)

A: We will use second derivative test to find the smallest distance among point (5,0) and curve

Q: wherey = x + C is a solution to this DE. What is the particular solution?

A: Let's find.

Q: Is the equation y’=y/x autonomous? True or false?

A: Given:The given equation is .To Find:We have to determine whether the given equation is autonomous…

Q: Evaluate y' if y = vtan x

A: We solve the problem by doing the derivative using the formula.

Q: what are the stable equilibria (X1 ,X2)?

A: Given that, Plants depend on microbial partners (bacteria and fungi) within soil to provide them…

Q: Evaluate * (1 – x²)3/2° 1 + c 3 1-x2 -1 + c /1 – x² O Option 4 Option 2 2 1 1 + c /1 – x² :+c 3 V1-…

A: ∫ xdx/(1-x2)3/2 here assume that  1-x2 = u -2x = du/dx xdx = -du/2 ∫ -du/2u3/2 ∫ -u-3/2du/2 2u-1/2/2…

Q: given that  x^2y^2+3x=y^3-1 use implicit differeniation to find the value of y'(1,2) a.3/2…

A: