6. (D³ + 2D²)y = 0; when x = 0, y = -3, y' = 0, y" = 12

Q: Calculate y" and y'''. y = 4t 3 - 9t 2 + 7

A: Given that  y = 4t3 - 9t2 + 7 We have to calculate y'' and y'''. First we find y'. y' = ddty     =…

Q: Differentiate. x4 y: 3 — х3 y' У -

A:

Q: calculate y" and y"'. y = 7 − 2x

A: Given function: y=7-2x

Q: Differentiate. y = In (6x? - 5x + 3) y' =O

A: Given: y=ln6x2-5x+3 We know that ddxlnx=1x…

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: 5. (D²+4)y=4 cot 2x

A: We use variation of parameters method to solve the given differential equation.

Q: Sx sech2 x² dx

A: Given:  Integral of xsech2x2

Q: Differentiate. et y = 8x2 y' =

A: Given:- y =ex /(8x2)  To find:- y'

Q: √√x²+9 dx

A: Give integral is ∫x3x2+94dx

Q: y"+y=sec³x

A: The given equation is: y"+y=sec3x

Q: What is the order of the equation y" y- (y')³=4?

A:

Q: 5. (x2 - y?)dx – 2xydy = 0 %3D

A:

Q: Y"+y=secxtanx

A: Given, y'' + y = secx tanx This is a second order linear, non-homogeneous ODE. We can write the…

Q: Calculate y" and y"'. y = x4 − 25x2 + 2x

A: Use the power rule and sum rule and difference rule of derivative:

Q: уху + ху %3D 7, у"

A: x.y+x.y=7we know thatddx(uv)=vdudx-udvdxv2    and ddx(u.v)=udvdx+vdudxdifferentiate…

Q: dy - (1+x)у -ху? .2 1.) х- dx

A:

Q: x²dx 3 2 3 (5-x') 2.

A:

Q: whats y" of y=15xcosx

A:

Q: Solve. х y" – 7y' = 6e6x

A:

Q: Зу" +y=0.

A:

Q: 1. Solve for 'x': vx + v2x +7 = 8

A: