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Solve the differential equation \[ y^{\prime \prime \prime}(t)+2 y^{\prime \prime}(t)+y^{\prime}(t)=0 \] |
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Answer» It's auxiliary equation is m3 + 2m2 + m = 0 ⇒ m(m2 + 2m + 1) = 0 ⇒ m(m + 1)2 = 0 ⇒ m = 0, -1, -1 ∴ y = C.F. = C1e0x + (C2 + C3x)e-x ⇒ y = C1 + (C2 + C3x)e-x which is solution of given differential equation. |
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