y ″ = − y 100. Assuming that the solution will be proportional to e λ x for some constant λ. Substitute y = e λ x y ″ = λ 2 e λ x into the differential equation to get. 100 λ 2 e λ x + e λ x = 0.

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A first order Differential Equation is Homogeneous when it can be in this form: dy dx = F ( y x ) We can solve it using Separation of Variables but first we create a new variable v = y x v = y x which

Now, assume that solutions to this differential equation will be in the form y(t) = ert y ( t) = e r t and plug this into the differential equation and with a little simplification we get

See the answer. Find the general solution to the homogeneous differential equations. a.) d 2 ydt 2−0 dydt +0 y =0. b.) d 2 ydt 2−14 dydt +49 y =0. The solutions have the form. y = C 1 f 1 ( t )+ C

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You'll get a detailed solution from a subject matter expert that helps you learn core concepts. See Answer. Find the general solution to the homogeneous differential equation: (d 2 y/dt 2 )+10