1(a)
Using Taylor's series, find y(0.4) where dy/dx = 1 + xy with y(0) = 2.
3 M
1(b)
Find the complementary function of
3 M
1(c)
Evaluate the following:
3 M
1(d)
Evaluate the following:
3 M
1(e)
Show that the following holds true:
4 M
1(f)
Using Euler's method, solve: dy/dx = x + y, y(0) =1. Find the value of y at x=1, taking h = 0.2
4 M
2(a)
Evaluate the following:
6 M
2(b)
Use Runge-Kutta method of fourth order to solve dy/dx=1/(x+y); y(0)=1. Find y(0.2) with h=0.1
6 M
2(c)
Solve the following:
8 M
3(a)
Solve the following:
6 M
3(b)
Solve the following using variation of parameters.
6 M
3(c)
Evaluate the following:
![](data:image/png;base64,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)
and hence deduce that:
and hence deduce that:
8 M
4(a)
Solve the following: (xy3+y)dx+2(x2 y2+x+y4 )dy=0
6 M
4(b)
Solve the following:
6 M
4(c)
Solve the following:
8 M
5(a)
In a circuit containing Inductance L, Resistance R, and Voltage E, the current i is L di/dt+Ri=E. Find i at time t. At t=0,i=0, L,R,E are constants.
6 M
5(b)
Change the order of integration:
6 M
5(c)
Evaluate the following
over the volume of a sphere x2 + y2 + z2 = a2
over the volume of a sphere x2 + y2 + z2 = a2
8 M
6(a)
Find the length of the parabola x2 = 4y which lies inside the circle x2 + y2 = 6y.
6 M
6(b)
Change into polar and evaluate:
6 M
6(c)
Evaluate the following
over the area of the triangle formed by x = 0, y = 0, x + y = 1.
over the area of the triangle formed by x = 0, y = 0, x + y = 1.
8 M
7(a)
Change the order of integration and evaluate
6 M
7(b)
Find the area outside the circle r=a and inside the cardioid r=a(1+cosθ)
6 M
7(c)
Find the volume common to the cylinders: x2 + y2 = a2, x2 + z2 = a2
8 M
More question papers from Applied Mathematics 2