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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solve the given DE or IVP (Initial-Value Problem).
a. 2y′ + y cot x = 8y-1 cos3 x
b. y′ = sin2 (3x − 3y + 1)
c. xy′ + y ln x = y ln y
d. x2 dy/dx = y2 + 5xy +
4x2