Resolveremos la siguiente ecuación. 𝐼𝐼 2𝑌 + 𝐼 20𝑌 + 51𝑌 = 0 𝑌 0 = 2 𝐼 𝑌 0 =0 SOLUCIÓN. 𝟐𝑺𝟐 𝒀 𝑺 − 𝟐𝑺𝒀 𝟎 − 𝟐𝒀𝑰 𝟎 + 𝟐𝟎𝑺𝒀 𝑺 − 𝟐𝟎𝒀 𝟎 + 𝟓𝟏𝒀 𝑺 = 𝟎 𝟐𝑺𝟐 𝒀 𝑺 − 𝟐𝑺𝒀 𝟎 − 𝟐𝒀𝑰 𝟎 + 𝟐𝟎𝑺𝒀 𝑺 − 𝟐𝟎𝒀 𝟎 + 𝟓𝟏𝒀 𝑺 = 𝟎 𝟐𝑺𝟐 𝒀 𝑺 − 𝟒𝑺 + 𝟐𝟎𝑺𝒀 𝑺 − 𝟒𝟎 + 𝟓𝟏𝒀 𝑺 = 𝟎 4𝑆 + 40 Y 𝑆 = 2 2𝑆 + 20𝑆 + 51 𝑌 𝑌 𝑌 −𝐼 4𝑆+40 2𝑆 2 +20𝑆+51 −𝐼 2𝑆+20 𝑆 2 +10𝑆+25.5 −𝐼 2𝑆+20 𝑆 =ʆ 𝑆 =ʆ 𝑆 =ʆ 1 2 𝑆 +10𝑆+25+ 2 𝑌 𝑆 =ʆ 2𝑆 + 20 −𝐼 𝑆2 𝑌 𝑌 𝑌 𝑇 =ʆ 𝑇 = 2ʆ 𝑇 = 2ʆ −𝐼 −𝐼 −𝐼 1 + 10𝑆 + 25 + 2 2𝑆 1 2 (𝑆+5) + 2 𝑆 1 2 (𝑆+5) + 2 𝑆 1 2 (𝑆+5) + 2 +ʆ + 20ʆ + 20 20 −𝐼 1 2 (𝑆+5) + 2 −𝐼 1 1 2 (𝑆+5) + 2 1 −𝐼 ∗ 1ʆ √ 2 1 2 1 2 (𝑆+5) + 2 √ 𝑌 𝑇 = 2𝑒 𝑌 −5𝑡 𝑇 = 2𝑒 1 cos√ 2 −5𝑡 Solución. 𝑌 𝑇 = 2𝑒 −5𝑡 cos 𝑡 + 20 ∗ 𝑡 cos + √2 𝑡 √2 1 1 √ 2 𝑒 20 2 𝑒 + 20 2 𝑒 −5𝑡 −5𝑡 −5𝑡 1 sin√ 𝑡 2 𝑡 sin √2 sin 𝑡 √2