1.3.3 Examples for the main algorithm

1.3.3.1 \(y^{\prime }+y=\sin \left ( x\right ) \) with one IC \(y\left ( 0\right ) =0\)
1.3.3.2 \(y^{\prime }+y=\sin \left ( x\right ) \) with one mixed IC \(y\left ( 0\right ) +y\left ( 1\right ) =0\)
1.3.3.3 \(y^{\prime }+y=\sin \left ( x\right ) \) with two IC \(y\left ( 0\right ) =0,y^{\prime }\left ( 0\right ) =0\)
1.3.3.4 \(y^{\prime }+y=\sin \left ( x\right ) \) with two IC \(y\left ( 0\right ) =0,y^{\prime }\left ( 0\right ) =1\)
1.3.3.5 \(y^{\prime \prime }+y=\sin \left ( x\right ) \) with one IC \(y\left ( 0\right ) =0\)
1.3.3.6 \(y^{\prime \prime }+y=\sin \left ( x\right ) \) with one mixed IC \(y\left ( 0\right ) +y\left ( 2\right ) =8\)
1.3.3.7 \(y^{\prime \prime }+y=\sin \left ( x\right ) \) with three IC \(y\left ( 0\right ) =0,y\left ( 1\right ) =0,y\left ( 2\right ) =5\)