The second order differential equation is
y' + x = y2
y'y'' + y = sin(x)
y''' + y'' + y = 0
y' = y
The solution of the differential equation is
x2loge(x) + y = c
xloge(x) + cx = y
x2loge(x) - y = c
xloge(x) + y = cx
An integrating factor of the differential equation , is
- x
C.
Withthehelp of Trapezoidal rule fornumerical integration and the following table
x | 0 | 0.25 | 0.50 | 0.75 | 1 |
f(x) | 0 | 0.625 | 0.2500 | 0.5625 | 1 |
the value of is
0.35342
0.34375
0.34457
0.33334
The maximum value of z = 4x + 2y subject to the constraints 2x + 3y 18, x + y 10, x, y 0
36
40
20
None of these
The maximum value of = 3x + 4y, subject to the conditions x + y 40, x + 2y 60, x, y 0, is
130
140
40
120