A treatise on Diﬀerential Equations by A. R. Forsyth. 6th edition. 1929. Macmillan Co. ltd. New York, reprinted 1956

2.20.34 A treatise on Diﬀerential Equations by A. R. Forsyth. 6th edition. 1929. Macmillan Co. ltd. New York, reprinted 1956

Column notations: A is ODE degree. B is Program Number of solutions generated. C is CAS Number of solutions generated.

Table 2.446: A treatise on Diﬀerential Equations by A. R. Forsyth. 6th edition. 1929. Macmillan Co. ltd. New York, reprinted 1956


#	ODE	A	B	C	Program classiﬁcation	CAS classiﬁcation	Solved?	Veriﬁed?	time (sec)

5471	\[ {}x \left (-x^{2}+2\right ) y^{\prime \prime }-\left (x^{2}+4 x +2\right ) \left (\left (1-x \right ) y^{\prime }+y\right ) = 0 \]	1	1	1	second order series method. Regular singular point. Diﬀerence is integer	[[_2nd_order, _with_linear_symmetries]]	✓	✓	1.262

5472	\[ {}x^{2} \left (1+x \right ) y^{\prime \prime }-\left (2 x +1\right ) \left (-y+x y^{\prime }\right ) = 0 \]	1	1	1	second order series method. Regular singular point. Repeated root	[[_2nd_order, _with_linear_symmetries]]	✓	✓	1.035

5473	\[ {}x^{3} \left (1+x \right ) y^{\prime \prime \prime }-\left (4 x +2\right ) x^{2} y^{\prime \prime }+\left (4+10 x \right ) x y^{\prime }-\left (4+12 x \right ) y = 0 \]	1	0	1	unknown	[[_3rd_order, _with_linear_symmetries]]	✗	N/A	0.0

5474	\[ {}x^{3} \left (x^{2}+1\right ) y^{\prime \prime \prime }-\left (4 x^{2}+2\right ) x^{2} y^{\prime \prime }+\left (10 x^{2}+4\right ) x y^{\prime }-\left (12 x^{2}+4\right ) y = 0 \]	1	0	1	unknown	[[_3rd_order, _with_linear_symmetries]]	✗	N/A	0.0

5475	\[ {}2 \left (2-x \right ) x^{2} y^{\prime \prime }-\left (4-x \right ) x y^{\prime }+\left (-x +3\right ) y = 0 \]	1	1	1	second order series method. Regular singular point. Diﬀerence is integer	[[_2nd_order, _with_linear_symmetries]]	✓	✓	1.068

5476	\[ {}\left (1-x \right ) x^{2} y^{\prime \prime }+\left (5 x -4\right ) x y^{\prime }+\left (6-9 x \right ) y = 0 \]	1	1	1	second order series method. Regular singular point. Diﬀerence is integer	[[_2nd_order, _with_linear_symmetries]]	✓	✓	2.832

5477	\[ {}x y^{\prime \prime }+\left (4 x^{2}+1\right ) y^{\prime }+4 x \left (x^{2}+1\right ) y = 0 \]	1	1	1	second order series method. Regular singular point. Repeated root	[[_2nd_order, _with_linear_symmetries]]	✓	✓	1.019

5478	\[ {}x^{2} y^{\prime \prime }+4 \left (x +a \right ) y = 0 \]	1	1	1	second order series method. Regular singular point. Diﬀerence not integer	[[_2nd_order, _with_linear_symmetries]]	✓	✓	1.258

5479	\[ {}x y^{\prime \prime }+\left (x^{3}+1\right ) y^{\prime }+b x y = 0 \]	1	1	1	second order series method. Regular singular point. Repeated root	[[_2nd_order, _with_linear_symmetries]]	✓	✓	1.65

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