Differential Equations
3y-2yx^2 [ 1 + (ln (2x^3 / 3y^2))^2 ]dx - 2xdy =0
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3y-2yx^2 [ 1 + (ln (2x^3 / 3y^2))^2 ]dx - 2xdy =0
The given two-parameter family is a solution of the indicated differential equation on the
interval (−∞,∞). Determine whether a member of the family can be found that satisfies the
initial conditions.
y = c1e^x cos x + c2e^x sin x; y" − 2y' + 2y = 0,
i. y(0) = 1, y'(π) = 0
ii. y(0) = 1, y(π) = −1
2xy' + y³ e^(-2x) = 2xy
Find each member and reactions. (by joint method)
What is line organisation and line and staff organisation
(1+x) (y' + y²)-y=0
Let
f1(x) = 1 + x^3 for x ≤ 0 ,1 for x ≥ 0
f2(x)= 1 for x ≤ 0, 1 + x^3 for x ≥ 0
f3(x)= 3 + x^3 for all x.
show that
a) f, f' , f", are continous for all x for each f1, f2, f3.
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