32. Y"(t) + 4Y(t) = 9t, Y(0) 0, Y'(0) = 7. Ans. Y(t) = 3t+2 sin 2t

Q: Find y' at the point (6, 6) where x sin(x? – y²) + 33 = x? – 3.

A:

Q: a particle moves along a curve y = (2x² + 5x)°, calculatey (0) and what is the interpretation of the…

A: Let us considre the function y=f(x) The derivative the function is denoted as dydx=f'(x) Derivative…

Q: Find y' and y". y - In(x + VB+ x²) / 8 + x² 1 y' = V 8 +x2 y" II

A: Given: y=lnx+8+x2

Q: 13. Find y' for sin(xy²) + x² = y². %3D

A:

Q: Find y' and y". In(7x) y = x7 y' = y" %3D

A: The given function is: y=ln(7x)x7 Therefore, y'=1x7ddx(ln(7x))+ln(7x)ddx1x7    =1x717x·7+ln(7x)-7x8…

Q: 5y + sin y = x²

A:

Q: 8. Find y'if y = x³ +sin (x)

A:

Q: Find f if f"(t) = 2e¹ + 3 sin(t), f(0) = −4, ƒ(ñ) = 9. f(t) = 2e^t-3sint-6

A:

Q: 3y' –4x²y+ xy = -5 %3D

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: 2.x²y+ 3xy? = 2x + 55

A: We will find the value of dy/dx and the equation of the tangent line at point (5,1) in the following…

Q: 7. Find y'if y=x³+ sin (x)

A: given

Q: Find y' if y=Cos (sinx)

A:

Q: Calculate y' given y below. (a) xey = y − 1. (b) y = (cos x)^x (c) y =(√sin^3(√2x))

A: a). Differentiate separately both sides of the equation (treat y as a function of…