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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
\(\left ( 1+at\right ) y^{\prime }+y=t,y(1)=0\)
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