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5.2 Problems
identically: s
3. f(x) = 0, g(x) = sin(x), h(x) = e
6. f = e^gx = cosh(x), h(x) = sinh(x)
Interval. 7. f(x) = 1, g(x) = x, h(x) = x on the real line
f(x) = xg(x) = cos(ln(x)), h(x) = sin(ln(x)), x > 0
In Problems 13 through 20, a third-order homogeneous linear equation and three linearly independent solutions are given. Find a particular solution satisfying the given initial conditions.
13. y'' + 2y' - y - 2y = 0; y(0) = 1, y'(0) = 2, y''(0) = 0;
y = e^x, y^3 = xe
y = cos(3x), y^3 = sin(3x)