1.3 Examples with time varying coefficients

1.3.1 Example 1 \(y^{\prime }-ty=0,y\left ( 0\right ) =0\)
1.3.2 Example 2 \(ty^{\prime }+y=0,y\left ( 0\right ) =0\)
1.3.3 Example 3 \(ty^{\prime }+y=0,y\left ( 0\right ) =y_{0}\)
1.3.4 Example 4 \(ty^{\prime }+y=0,y\left ( x_{0}\right ) =y_{0}\)
1.3.5 Example 5 \(ty^{\prime }+y=0\)
1.3.6 Example 6 \(ty^{\prime }+y=0,y\left ( 1\right ) =5\)
1.3.7 Example 7 \(ty^{\prime }+y=\sin \left ( t\right ) ,y\left ( 1\right ) =0\)
1.3.8 Example 8 \(ty^{\prime }+y=t,y\left ( 1\right ) =0\)
1.3.9 Example 9 \(ty^{\prime }+y=t,y(1)=1\)
1.3.10 Example 10 \(y^{\prime }+t^{2}y=0,y(0)=0\)
1.3.11 Example 11 \(\left ( 1+at\right ) y^{\prime }+y=t,y(1)=0\)