4.27. Find an explicit solution for y' = xe¯³, y(0) : = 1.

Q: 2) Find the derivatives of a) y = 7 - 6x-x² b) y - ³x 8 √x

A: Given :(a)y=7-6x-x2(b)y=-8x

Q: y' = y = eP(p + p√p)

A:

Q: Choose the correct answer If x2 + y2 = 9, then y'=...  -y/x  y/x  -x/y  x/y

A: We have to find y'

Q: * Find y as a function of æ if y" – 8y" – y' + 8y = 0, y(0) = 4, y'(0) = -6, y" (0) = 130. y(x) =

A:

Q: Differentiate. y = ³√√x³+3x+1.x4

A: Given function y = x3 + 3x + 13.x4

Q: Determine 4sin(x); the value of the arbitrary constants y(x) = C₁e* + c₂e¯* + y(0) = 1, y'(0) = -1…

A:

Q: - 4. 3y(x² − 1)dx + (x³ + 8y − 3x)dy = 0; when x = 0, y = 1

A:

Q: 5. Find y'. y = 3x² – 14x + 42

A:

Q: .3 t +y3

A: Derivative is below

Q: Find y as a function of t if y(3) = 2, y = y'(3) = 2. 25y" +90y + 162y = 0,

A: We find y as a function of t 25y'' +90y'+162y=0,y(3)= 2, y'(3)=2

Q: Solve the IVP. (35 53 X' = X with X(0) = - (4).

A:

Q: 4.25. Solve y' = (y − 1)(y + 1) for y(0) = 3.

A: Step 3: Step 4: