Problems 101 to 200

Table 4.547: Second order non-linear ODE


#	ODE	Mathematica	Maple	Sympy

7765	\[ {} y^{\prime \prime } = 1+{y^{\prime }}^{2} \]	✓	✓	✓

7766	\[ {} y^{\prime \prime } = -\frac {1}{2 {y^{\prime }}^{2}} \]	✓	✓	✓

7767	\[ {} y^{\prime \prime }+\sin \left (y\right ) = 0 \]	✓	✓	✗

7768	\[ {} y^{\prime \prime }+\sin \left (y\right ) = 0 \]	✗	✓	✗

7824	\[ {} y^{\prime \prime } y^{\prime } = x \left (1+x \right ) \]	✓	✓	✓

7905	\[ {} {y^{\prime }}^{2}+y y^{\prime \prime } = 0 \]	✓	✓	✗

7906	\[ {} x y y^{\prime \prime } = {y^{\prime }}^{3}+y^{\prime } \]	✓	✗	✗

7908	\[ {} x^{2} y^{\prime \prime } = 2 x y^{\prime }+{y^{\prime }}^{2} \]	✓	✓	✓

7909	\[ {} 2 y y^{\prime \prime } = 1+{y^{\prime }}^{2} \]	✓	✓	✗

7910	\[ {} y y^{\prime \prime }-{y^{\prime }}^{2} = 0 \]	✓	✓	✗

7912	\[ {} \left (x^{2}+2 y^{\prime }\right ) y^{\prime \prime }+2 x y^{\prime } = 0 \]	✓	✓	✓

7913	\[ {} y y^{\prime \prime } = y^{2} y^{\prime }+{y^{\prime }}^{2} \]	✓	✓	✗

7914	\[ {} y^{\prime \prime } = y^{\prime } {\mathrm e}^{y} \]	✗	✓	✗

7915	\[ {} y^{\prime \prime } = 1+{y^{\prime }}^{2} \]	✓	✓	✓

7916	\[ {} y^{\prime \prime }+{y^{\prime }}^{2} = 1 \]	✓	✓	✗

7933	\[ {} y y^{\prime \prime }-{y^{\prime }}^{2} = 0 \]	✓	✓	✗

7934	\[ {} x y^{\prime \prime } = y^{\prime }-2 {y^{\prime }}^{3} \]	✓	✓	✓

7935	\[ {} y y^{\prime \prime }+y^{\prime } = 0 \]	✓	✓	✗

8071	\[ {} y^{\prime \prime }+\sin \left (y\right ) = 0 \]	✓	✓	✗

8489	\[ {} y^{\prime \prime } = x {y^{\prime }}^{3} \]	✓	✓	✓

8490	\[ {} x^{2} y^{\prime \prime }+{y^{\prime }}^{2}-2 x y^{\prime } = 0 \]	✓	✓	✓

8491	\[ {} x^{2} y^{\prime \prime }+{y^{\prime }}^{2}-2 x y^{\prime } = 0 \]	✓	✓	✓

8492	\[ {} {y^{\prime }}^{2}+y y^{\prime \prime } = 0 \]	✓	✓	✗

8493	\[ {} y^{2} y^{\prime \prime }+{y^{\prime }}^{3} = 0 \]	✓	✓	✗

8494	\[ {} \left (y+1\right ) y^{\prime \prime } = {y^{\prime }}^{2} \]	✓	✓	✗

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

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

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

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

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

8514	\[ {} y^{\prime \prime } = 1+{y^{\prime }}^{2} \]	✓	✓	✓

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

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

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

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

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

8523	\[ {} y^{\prime \prime } = 2 x +\left (x^{2}-y^{\prime }\right )^{2} \]	✓	✓	✓

8524	\[ {} {y^{\prime \prime }}^{2}-2 y^{\prime \prime }+{y^{\prime }}^{2}-2 x y^{\prime }+x^{2} = 0 \]	✗	✓	✗

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

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

8527	\[ {} 3 y y^{\prime } y^{\prime \prime } = {y^{\prime }}^{3}-1 \]	✓	✓	✗

8528	\[ {} 4 y {y^{\prime }}^{2} y^{\prime \prime } = {y^{\prime }}^{4}+3 \]	✓	✓	✗

8774	\[ {} y y^{\prime \prime } = 1 \]	✓	✓	✓

8775	\[ {} y y^{\prime \prime } = x \]	✗	✗	✗

8776	\[ {} y^{2} y^{\prime \prime } = x \]	✗	✓	✗

8778	\[ {} 3 y y^{\prime \prime } = \sin \left (x \right ) \]	✗	✗	✗

8779	\[ {} 3 y y^{\prime \prime }+y = 5 \]	✓	✓	✗

8780	\[ {} a y y^{\prime \prime }+b y = c \]	✓	✓	✗

8781	\[ {} a y^{2} y^{\prime \prime }+b y^{2} = c \]	✓	✓	✓

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

8803	\[ {} y^{\prime \prime }-y y^{\prime } = 2 x \]	✓	✓	✗

8879	\[ {} \left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2} = 0 \]	✓	✓	✓

8880	\[ {} \left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2} = x \]	✗	✓	✗

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

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

9087	\[ {} {y^{\prime \prime }}^{2}+y^{\prime } = 1 \]	✓	✓	✓

9088	\[ {} y^{\prime \prime }+{y^{\prime }}^{2} = 1 \]	✓	✓	✗

9090	\[ {} {y^{\prime \prime }}^{2}+y^{\prime } = x \]	✓	✓	✗

9091	\[ {} y^{\prime \prime }+{y^{\prime }}^{2} = x \]	✓	✓	✗

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

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

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

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

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

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

4.6.2 Problems 101 to 200