IGNOU PHE 5 2026 - Solve the initial value problem:

Question

Solve the initial value problem:

$\frac{d^2x}{dt^2} - 3\frac{dx}{dt} - 10x = 0, \quad x(0) = 1, \quad \dot{x}(0) = 0$

29 Jan 2026

Answer :

Word Count : 204

The differential equation is [ \frac{d^2 x}{dt^2} - 3 \frac{dx}{dt} - 10 x = 0, \quad x(0) = 1, \quad \dot{x}(0) = 0. ] Assume a solution of the form (x(t) = e^{rt}). Substituting gives the characteristic equation: [ r^2 - 3r - 10 = 0. ] Solve the quadratic: [ r = \frac{3 \pm \sqrt{(-3)^2 - 4(1)(-10)}}{2} = \frac{3 \pm \sqrt{9 +

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