1.2 Examples solving using Laplace transform for constant coefficients ode

1.2.1 Example 1 \(y^{\prime }-2y=6e^{5t},y\left ( 0\right ) =3\)
1.2.2 Example 2 \(y^{\prime }-6y=0,y\left ( -1\right ) =4\)
1.2.3 Example 3 \(y^{\prime }+y=\sin \left ( t\right ) ,y\left ( 1\right ) =y_{0}\)