exercise:86ed3ad9f7: Difference between revisions
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<ul style{{=}}"list-style-type:lower-alpha" | <ul style{{=}}"list-style-type:lower-alpha"> | ||
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Solve the homogeneous differential equation | Solve the homogeneous differential equation | ||
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. | . | ||
</math></li> | </math></li> | ||
<li> | <li> | ||
Substitute the linear polynomial <math>Ax+B</math> for <math>y</math> | Substitute the linear polynomial <math>Ax+B</math> for <math>y</math> | ||
in the nonhomogeneous differential equation | in the nonhomogeneous differential equation | ||
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of the differential equation.</li> | of the differential equation.</li> | ||
<li>Show that the function which is the sum of the | <li>Show that the function which is the sum of the | ||
solutions found in | solutions found in (a) and (b) is also a solution to the | ||
differential equation in (b).</li> | |||
differential equation in | |||
</ul> | </ul> | ||
Latest revision as of 02:00, 24 November 2024
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[/math]
-
Solve the homogeneous differential equation
[[math]] \deriv2y - 8 \dydx + 12y = 0 . [[/math]]
-
Substitute the linear polynomial [math]Ax+B[/math] for [math]y[/math]
in the nonhomogeneous differential equation
[[math]] \deriv2y - 8\dydx + 12y = 24x + 12 . [[/math]]Hence find values of [math]A[/math] and [math]B[/math] for which this polynomial is a particular solution of the differential equation.
- Show that the function which is the sum of the solutions found in (a) and (b) is also a solution to the differential equation in (b).