Problems 101 to 200

Table 4.875: Second order, non-linear and homogeneous


#	ODE	Mathematica	Maple	Sympy

8495	\[ {} 2 a y^{\prime \prime }+{y^{\prime }}^{3} = 0 \]	✓	✓	✓

8498	\[ {} y^{\prime \prime } = 2 y {y^{\prime }}^{3} \]	✓	✓	✗

8499	\[ {} y^{\prime \prime } y+{y^{\prime }}^{3}-{y^{\prime }}^{2} = 0 \]	✓	✓	✗

8501	\[ {} y^{\prime \prime } y+{y^{\prime }}^{3} = 0 \]	✓	✓	✗

8503	\[ {} y^{\prime \prime } = x {y^{\prime }}^{2} \]	✓	✓	✓

8504	\[ {} y^{\prime \prime } = x {y^{\prime }}^{2} \]	✓	✓	✓

8505	\[ {} y^{\prime \prime } = -{\mathrm e}^{-2 y} \]	✓	✓	✗

8506	\[ {} y^{\prime \prime } = -{\mathrm e}^{-2 y} \]	✓	✓	✗

8507	\[ {} 2 y^{\prime \prime } = \sin \left (2 y\right ) \]	✗	✗	✗

8508	\[ {} 2 y^{\prime \prime } = \sin \left (2 y\right ) \]	✗	✗	✗

8510	\[ {} y^{\prime \prime } = {y^{\prime }}^{2} \]	✓	✓	✓

8511	\[ {} y^{\prime \prime } = {\mathrm e}^{x} {y^{\prime }}^{2} \]	✓	✓	✓

8512	\[ {} 2 y^{\prime \prime } = {y^{\prime }}^{3} \sin \left (2 x \right ) \]	✓	✓	✗

8513	\[ {} x^{2} y^{\prime \prime }+{y^{\prime }}^{2} = 0 \]	✓	✓	✓

8515	\[ {} y^{\prime \prime } = \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} \]	✓	✓	✗

8516	\[ {} y^{\prime \prime } y = {y^{\prime }}^{2} \left (1-y^{\prime } \sin \left (y\right )-y y^{\prime } \cos \left (y\right )\right ) \]	✓	✓	✗

8517	\[ {} \left (1+y^{2}\right ) y^{\prime \prime }+{y^{\prime }}^{3}+y^{\prime } = 0 \]	✓	✓	✗

8518	\[ {} \left (y^{\prime \prime } y+1+{y^{\prime }}^{2}\right )^{2} = \left (1+{y^{\prime }}^{2}\right )^{3} \]	✓	✓	✗

8519	\[ {} x^{2} y^{\prime \prime } = y^{\prime } \left (2 x -y^{\prime }\right ) \]	✓	✓	✓

8520	\[ {} x^{2} y^{\prime \prime } = y^{\prime } \left (3 x -2 y^{\prime }\right ) \]	✓	✓	✓

8521	\[ {} x y^{\prime \prime } = y^{\prime } \left (2-3 x y^{\prime }\right ) \]	✓	✓	✓

8522	\[ {} x^{4} y^{\prime \prime } = y^{\prime } \left (y^{\prime }+x^{3}\right ) \]	✓	✓	✓

8525	\[ {} {y^{\prime \prime }}^{2}-x y^{\prime \prime }+y^{\prime } = 0 \]	✓	✓	✓

8526	\[ {} {y^{\prime \prime }}^{3} = 12 y^{\prime } \left (x y^{\prime \prime }-2 y^{\prime }\right ) \]	✗	✓	✗

8799	\[ {} y^{\prime \prime } = \frac {1}{y}-\frac {x y^{\prime }}{y^{2}} \]	✓	✓	✗

8881	\[ {} \left (x^{2}+1\right ) y^{\prime \prime }+1+x {y^{\prime }}^{2} = 1 \]	✓	✓	✓

8882	\[ {} \left (x^{2}+1\right ) y^{\prime \prime }+y {y^{\prime }}^{2} = 0 \]	✗	✗	✗

8883	\[ {} \left (x^{2}+1\right ) y^{\prime \prime }+{y^{\prime }}^{2} = 0 \]	✓	✓	✓

8884	\[ {} y^{\prime \prime }+{y^{\prime }}^{2} \sin \left (y\right ) = 0 \]	✓	✓	✗

8885	\[ {} \left (x^{2}+1\right ) y^{\prime \prime }+{y^{\prime }}^{3} = 0 \]	✓	✓	✓

8962	\[ {} y^{\prime \prime } = A y^{{2}/{3}} \]	✓	✓	✓

8983	\[ {} y^{\prime \prime }+{\mathrm e}^{y} = 0 \]	✓	✓	✓

9084	\[ {} {y^{\prime \prime }}^{2}+y^{\prime } = 0 \]	✓	✓	✓

9085	\[ {} y^{\prime \prime }+{y^{\prime }}^{2} = 0 \]	✓	✓	✓

9093	\[ {} {y^{\prime \prime }}^{2}+y^{\prime }+y = 0 \]	✗	✗	✗

9094	\[ {} y^{\prime \prime }+{y^{\prime }}^{2}+y = 0 \]	✓	✓	✗

9116	\[ {} y {y^{\prime \prime }}^{2}+y^{\prime } = 0 \]	✓	✓	✗

9117	\[ {} y {y^{\prime \prime }}^{2}+{y^{\prime }}^{3} = 0 \]	✓	✓	✗

9118	\[ {} y^{2} {y^{\prime \prime }}^{2}+y^{\prime } = 0 \]	✓	✓	✗

9119	\[ {} y {y^{\prime \prime }}^{4}+{y^{\prime }}^{2} = 0 \]	✓	✓	✗

9120	\[ {} y^{3} {y^{\prime \prime }}^{2}+y y^{\prime } = 0 \]	✓	✓	✓

9121	\[ {} y^{\prime \prime } y+{y^{\prime }}^{3} = 0 \]	✓	✓	✗

9122	\[ {} y {y^{\prime \prime }}^{3}+y^{3} y^{\prime } = 0 \]	✓	✓	✓

9123	\[ {} y {y^{\prime \prime }}^{3}+y^{3} {y^{\prime }}^{5} = 0 \]	✓	✓	✓

9124	\[ {} y^{\prime \prime }+x y^{\prime }+y {y^{\prime }}^{2} = 0 \]	✓	✓	✗

9125	\[ {} y^{\prime \prime }+\sin \left (x \right ) y^{\prime }+y {y^{\prime }}^{2} = 0 \]	✓	✓	✗

9126	\[ {} y^{\prime \prime }+\left (1-x \right ) y^{\prime }+y^{2} {y^{\prime }}^{2} = 0 \]	✓	✓	✗

9127	\[ {} y^{\prime \prime }+\left (\sin \left (x \right )+2 x \right ) y^{\prime }+\cos \left (y\right ) y {y^{\prime }}^{2} = 0 \]	✓	✓	✗

9128	\[ {} y^{\prime } y^{\prime \prime }+y^{2} = 0 \]	✓	✓	✗

9129	\[ {} y^{\prime } y^{\prime \prime }+y^{n} = 0 \]	✓	✓	✗

9131	\[ {} y^{\prime \prime }+\left (x +3\right ) y^{\prime }+\left (y^{2}+3\right ) {y^{\prime }}^{2} = 0 \]	✓	✓	✗

9132	\[ {} y^{\prime \prime }+x y^{\prime }+y {y^{\prime }}^{2} = 0 \]	✓	✓	✗

9133	\[ {} y^{\prime \prime }+\sin \left (x \right ) y^{\prime }+{y^{\prime }}^{2} = 0 \]	✓	✓	✓

9134	\[ {} 3 y^{\prime \prime }+\cos \left (x \right ) y^{\prime }+{y^{\prime }}^{2} \sin \left (y\right ) = 0 \]	✓	✓	✗

9135	\[ {} 10 y^{\prime \prime }+x^{2} y^{\prime }+\frac {3 {y^{\prime }}^{2}}{y} = 0 \]	✓	✓	✗

9136	\[ {} 10 y^{\prime \prime }+\left ({\mathrm e}^{x}+3 x \right ) y^{\prime }+\frac {3 \,{\mathrm e}^{y} {y^{\prime }}^{2}}{\sin \left (y\right )} = 0 \]	✓	✓	✗

9159	\[ {} x^{2} y^{\prime \prime }+\left (x y^{\prime }-y\right )^{2} = 0 \]	✓	✓	✗

11551	\[ {} y^{\prime \prime }-y^{2} = 0 \]	✓	✓	✓

11552	\[ {} y^{\prime \prime }-6 y^{2} = 0 \]	✓	✓	✓

11554	\[ {} y^{\prime \prime }-6 y^{2}+4 y = 0 \]	✓	✓	✗

11557	\[ {} y^{\prime \prime }-a y^{3} = 0 \]	✓	✓	✓

11561	\[ {} y^{\prime \prime }+a \,x^{r} y^{2} = 0 \]	✗	✗	✗

11562	\[ {} y^{\prime \prime }+6 a^{10} y^{11}-y = 0 \]	✓	✓	✗

11563	\[ {} y^{\prime \prime }-\frac {1}{\left (y^{2} a +b x y+c \,x^{2}+\alpha y+\beta x +\gamma \right )^{{3}/{2}}} = 0 \]	✗	✓	✗

11564	\[ {} y^{\prime \prime }-{\mathrm e}^{y} = 0 \]	✓	✓	✓

11565	\[ {} y^{\prime \prime }+a \,{\mathrm e}^{x} \sqrt {y} = 0 \]	✗	✗	✗

11566	\[ {} y^{\prime \prime }+{\mathrm e}^{x} \sin \left (y\right ) = 0 \]	✗	✗	✗

11567	\[ {} y^{\prime \prime }+a \sin \left (y\right ) = 0 \]	✓	✓	✗

11570	\[ {} y^{\prime \prime } = \frac {f \left (\frac {y}{\sqrt {x}}\right )}{x^{{3}/{2}}} \]	✓	✓	✗

11571	\[ {} y^{\prime \prime }-3 y^{\prime }-y^{2}-2 y = 0 \]	✗	✗	✗

11572	\[ {} y^{\prime \prime }-7 y^{\prime }-y^{{3}/{2}}+12 y = 0 \]	✗	✗	✗

11573	\[ {} y^{\prime \prime }+5 a y^{\prime }-6 y^{2}+6 a^{2} y = 0 \]	✓	✓	✗

11574	\[ {} y^{\prime \prime }+3 a y^{\prime }-2 y^{3}+2 a^{2} y = 0 \]	✓	✓	✗

11575	\[ {} y^{\prime \prime }-\frac {\left (3 n +4\right ) y^{\prime }}{n}-\frac {2 \left (n +1\right ) \left (n +2\right ) y \left (y^{\frac {n}{n +1}}-1\right )}{n^{2}} = 0 \]	✗	✗	✗

11576	\[ {} y^{\prime \prime }+a y^{\prime }+b y^{n}+\frac {\left (a^{2}-1\right ) y}{4} = 0 \]	✗	✗	✗

11577	\[ {} y^{\prime \prime }+a y^{\prime }+b \,x^{v} y^{n} = 0 \]	✗	✗	✗

11579	\[ {} y^{\prime \prime }+a y^{\prime }+f \left (x \right ) \sin \left (y\right ) = 0 \]	✗	✗	✗

11580	\[ {} y^{\prime \prime }+y y^{\prime }-y^{3} = 0 \]	✓	✓	✗

11581	\[ {} y^{\prime \prime }+y y^{\prime }-y^{3}+a y = 0 \]	✓	✓	✗

11582	\[ {} y^{\prime \prime }+\left (y+3 a \right ) y^{\prime }-y^{3}+y^{2} a +2 a^{2} y = 0 \]	✓	✓	✗

11583	\[ {} y^{\prime \prime }+\left (y+3 f \left (x \right )\right ) y^{\prime }-y^{3}+y^{2} f \left (x \right )+y \left (f^{\prime }\left (x \right )+2 f \left (x \right )^{2}\right ) = 0 \]	✗	✗	✗

11584	\[ {} y^{\prime \prime }+\left (3 y+f \left (x \right )\right ) y^{\prime }+y^{3}+y^{2} f \left (x \right ) = 0 \]	✓	✓	✗

11586	\[ {} y^{\prime \prime }-\left (3 y+f \left (x \right )\right ) y^{\prime }+y^{3}+y^{2} f \left (x \right ) = 0 \]	✓	✓	✗

11587	\[ {} y^{\prime \prime }-2 a y y^{\prime } = 0 \]	✓	✓	✗

11588	\[ {} y^{\prime \prime }+a y y^{\prime }+b y^{3} = 0 \]	✓	✓	✗

11589	\[ {} y^{\prime \prime }+a {y^{\prime }}^{2}+b y = 0 \]	✓	✓	✗

11590	\[ {} y^{\prime \prime }+a {y^{\prime }}^{2}+b y^{\prime }+c y = 0 \]	✗	✗	✗

11591	\[ {} y^{\prime \prime }+a {y^{\prime }}^{2}+b \sin \left (y\right ) = 0 \]	✓	✓	✗

11592	\[ {} y^{\prime \prime }+a y^{\prime } {\| y^{\prime }\|}+b \sin \left (y\right ) = 0 \]	✗	✗	✗

11593	\[ {} y^{\prime \prime }+a y {y^{\prime }}^{2}+b y = 0 \]	✓	✓	✗

11594	\[ {} y^{\prime \prime }+a y \left (1+{y^{\prime }}^{2}\right )^{2} = 0 \]	✓	✓	✗

11595	\[ {} y^{\prime \prime }-a \left (x y^{\prime }-y\right )^{v} = 0 \]	✓	✓	✗

11596	\[ {} y^{\prime \prime }-k \,x^{a} y^{b} {y^{\prime }}^{r} = 0 \]	✗	✗	✗

11597	\[ {} y^{\prime \prime } = a \sqrt {1+{y^{\prime }}^{2}} \]	✓	✓	✗

11599	\[ {} y^{\prime \prime } = a \sqrt {{y^{\prime }}^{2}+b y^{2}} \]	✓	✓	✗

11600	\[ {} y^{\prime \prime } = a \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} \]	✓	✓	✗

11601	\[ {} y^{\prime \prime }-2 a x \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} = 0 \]	✓	✓	✗

11602	\[ {} y^{\prime \prime }-a y \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} = 0 \]	✓	✓	✗

11603	\[ {} y^{\prime \prime } = 2 a \left (c +b x +y\right ) \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} \]	✓	✓	✗

11604	\[ {} y^{\prime \prime }+y^{3} y^{\prime }-y y^{\prime } \sqrt {y^{4}+4 y^{\prime }} = 0 \]	✓	✓	✗

4.17.2 Problems 101 to 200