d^2y/dx^2 − dy/dx − 3/4 y = 0,
y(0) = 1, dy/dx(0) = 0,
Convert the initial value problem into a set of two coupled
first-order initial value problems
and find the exact solution to the differential equatiion
Evaluate or solve the following
A) dy/dx=
-(2x2+y2)/(2xy+3y2)
B)dy/dx=(1+y2)/(1+x2)xy
C) (x2+1)dy/dx+2xy=4x2 given that when
x=3,y=4
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Using Runge-Kutta method of order 4 to approximate y(1) with
step size h = 0.1 and h = 0.2 respectively (keep 8 decimals):
dy/dx = x + arctan y, y(0) = 0.
Solutions: when h = 0.1, y(1) = 0.70398191. when h = 0.2, y(1) =
0.70394257.