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(Solved): Differential EquationsUse the substitutionx = etto transform the given Cauchy-Euler equation to a di ...
Differential Equations
Use the substitution
x = et
to transform the given Cauchy-Euler equation to a differential equation with constant coefficients. (Use yp for
| dy |
| dt |
and ypp for
| d2y |
| dt2 |
.)
x2y'' ? 15xy' + 64y = 0
(c1?+c2?ln(x))·x8
Solve the original equation by solving the new equation using the procedures in Sections 4.3-4.5.
y(x) =
(c1?+c2?ln(x))·x8
, x > 0
Use the substitution to transform the given Cauchy-Euler equation to a differential equation with constant coefficients. (Use for and for .) Solve the original equation by solving the new equation using the procedures in Sections 4.3-4.5.