Find dy/dx for a & b
a) sin x+cos y=1
b) cos x^2 = xe^y
c)Let f(x) = 5 /2 x^2 − e^x . Find the value of x for which the
second derivative f'' (x) equals zero.
d) For what value of the constant c is the function f continuous
on (−∞,∞)?
f(x) = {cx^2 + 2x, x < 2 ,
2x + 4, x ≥ 2}
Solve the initial value problem dy/dx = −(2x cos(x^2))y +
6(x^2)e^(− sin(x^2)) , y(0) = −5
Solve the initial value problem dy/dt = (6t^5/(1 + t^6))y + 7(1
+ t^6)^2 , y(1) = 8.
Find the general solution of dy/dt = (2/t)*y + 3t^2* cos3t
evaluate
C
(y + 4 sin x)
dx + (z2 + 8 cos
y) dy +
x3dz
where C is the curve
r(t) =
sin t, cos t, sin
2t
, 0 ≤ t ≤ 2π.
(Hint: Observe that C lies on the surface
z = 2xy.)
Consider the following first-order ODE dy/dx=x^2/y from x = 0 to
x = 2.4 with y(0) = 2. (a) solving with Euler’s explicit method
using h = 0.6 (b) solving with midpoint method using h = 0.6 (c)
solving with classical fourth-order Runge-Kutta method using h =
0.6. Plot the x-y curve according to your solution for both (a) and
(b).