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
x2 y" + (x2+x) y’
+(2x-1) y = 0,
Find the general solution of y1 with
r1 and calculate the coefficient up to
c4 and also find the general expression of the
recursion formula, (recursion formula for
y1)
Find the general solution of y2 based on
theorem 4.3.1. (Hint, set d2 = 0)
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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