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1.3
Examples for Frobenius series for first order ode
1.3.1
Example 1.
\(xy^{\prime }+y=0,y\left ( 0\right ) =1\)
1.3.2
Example 2.
\(xy^{\prime }+y=x\)
1.3.3
Example 3.
\(xy^{\prime }+y=1\)
1.3.4
Example 4.
\(xy^{\prime }+y=k\)
1.3.5
Example 5.
\(xy^{\prime }+y=\sin x\)
1.3.6
Example 6.
\(xy^{\prime }+y=x+x^{3}+2x^{4}\)
1.3.7
Example 7.
\(xy^{\prime }+y=\frac {1}{x}\)
1.3.8
Example 8.
\(xy^{\prime }+y=\frac {1}{x^{2}}\)
1.3.9
Example 9.
\(xy^{\prime }+y=3+x\)
1.3.10
Example 10.
\(xy^{\prime }+y=\frac {1}{x^{3}}\)
1.3.11
Example 11
\(y^{\prime }+2xy=\sqrt {x}\)
1.3.12
Example 12
\(y^{\prime }+2xy=\frac {1}{x}\)
1.3.13
Example 13
\(y^{\prime }=\frac {1}{x}\)
1.3.14
Example 14
\(y^{\prime }=\frac {1}{x^{2}}\)
1.3.15
Example 15
\(y^{\prime }+\frac {y}{x}=0\)
1.3.16
Example 16
\(\cos \left ( x\right ) y^{\prime }+\frac {1}{x}y=x\)
1.3.17
Example 17
\(xy^{\prime }+2xy=\sqrt {x}\)
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