Problems 10401 to 10500

Table 6.209: Main lookup table sequentially arranged


#	ODE	Mathematica	Maple	Sympy

10401	\[ {} {y^{\prime }}^{2}-3 x y^{{2}/{3}} y^{\prime }+9 y^{{5}/{3}} = 0 \]	✓	✓	✗

10402	\[ {} 2 {y^{\prime }}^{2}+\left (x -1\right ) y^{\prime }-y = 0 \]	✓	✓	✓

10403	\[ {} 2 {y^{\prime }}^{2}-2 x^{2} y^{\prime }+3 x y = 0 \]	✓	✓	✗

10404	\[ {} 3 {y^{\prime }}^{2}-2 x y^{\prime }+y = 0 \]	✓	✓	✗

10405	\[ {} 3 {y^{\prime }}^{2}+4 x y^{\prime }-y+x^{2} = 0 \]	✓	✓	✓

10406	\[ {} a {y^{\prime }}^{2}+b y^{\prime }-y = 0 \]	✓	✓	✓

10407	\[ {} a {y^{\prime }}^{2}+b \,x^{2} y^{\prime }+c x y = 0 \]	✓	✓	✗

10408	\[ {} a {y^{\prime }}^{2}+y y^{\prime }-x = 0 \]	✓	✓	✗

10409	\[ {} a {y^{\prime }}^{2}-y y^{\prime }-x = 0 \]	✓	✓	✗

10410	\[ {} x {y^{\prime }}^{2}-y = 0 \]	✓	✓	✓

10411	\[ {} x {y^{\prime }}^{2}-2 y+x = 0 \]	✓	✓	✓

10412	\[ {} x {y^{\prime }}^{2}-2 y^{\prime }-y = 0 \]	✓	✓	✗

10413	\[ {} x {y^{\prime }}^{2}+4 y^{\prime }-2 y = 0 \]	✓	✓	✗

10414	\[ {} x {y^{\prime }}^{2}+x y^{\prime }-y = 0 \]	✓	✓	✓

10415	\[ {} x {y^{\prime }}^{2}+y y^{\prime }+a = 0 \]	✓	✓	✗

10416	\[ {} x {y^{\prime }}^{2}+y y^{\prime }-x^{2} = 0 \]	✓	✓	✗

10417	\[ {} x {y^{\prime }}^{2}+y y^{\prime }+x^{3} = 0 \]	✓	✓	✗

10418	\[ {} x {y^{\prime }}^{2}+y y^{\prime }-y^{4} = 0 \]	✓	✓	✓

10419	\[ {} x {y^{\prime }}^{2}+\left (y-3 x \right ) y^{\prime }+y = 0 \]	✓	✓	✓

10420	\[ {} x {y^{\prime }}^{2}-y y^{\prime }+a = 0 \]	✓	✓	✗

10421	\[ {} x {y^{\prime }}^{2}-y y^{\prime }+a y = 0 \]	✓	✓	✗

10422	\[ {} x {y^{\prime }}^{2}+2 y y^{\prime }-x = 0 \]	✓	✓	✓

10423	\[ {} x {y^{\prime }}^{2}-2 y y^{\prime }+a = 0 \]	✓	✓	✗

10424	\[ {} x {y^{\prime }}^{2}-2 y y^{\prime }-x = 0 \]	✓	✓	✓

10425	\[ {} x {y^{\prime }}^{2}-2 y y^{\prime }+4 x = 0 \]	✓	✓	✓

10426	\[ {} x {y^{\prime }}^{2}-2 y y^{\prime }+2 y+x = 0 \]	✓	✓	✓

10427	\[ {} x {y^{\prime }}^{2}+a y y^{\prime }+b x = 0 \]	✓	✓	✓

10428	\[ {} \left (1+x \right ) {y^{\prime }}^{2}-\left (x +y\right ) y^{\prime }+y = 0 \]	✓	✓	✗

10429	\[ {} \left (3 x +1\right ) {y^{\prime }}^{2}-3 \left (y+2\right ) y^{\prime }+9 = 0 \]	✓	✓	✗

10430	\[ {} \left (3 x +5\right ) {y^{\prime }}^{2}-\left (3 y+x \right ) y^{\prime }+y = 0 \]	✓	✓	✗

10431	\[ {} a x {y^{\prime }}^{2}+\left (b x -a y+c \right ) y^{\prime }-b y = 0 \]	✓	✓	✗

10432	\[ {} a x {y^{\prime }}^{2}-\left (a y+b x -a -b \right ) y^{\prime }+b y = 0 \]	✓	✓	✗

10433	\[ {} \left (\operatorname {a2} x +\operatorname {c2} \right ) {y^{\prime }}^{2}+\left (\operatorname {a1} x +\operatorname {b1} y+\operatorname {c1} \right ) y^{\prime }+\operatorname {a0} x +\operatorname {b0} y+\operatorname {c0} = 0 \]	✗	✓	✗

10434	\[ {} x^{2} {y^{\prime }}^{2}-y^{4}+y^{2} = 0 \]	✓	✓	✓

10435	\[ {} \left (x y^{\prime }+a \right )^{2}-2 a y+x^{2} = 0 \]	✓	✓	✗

10436	\[ {} \left (x y^{\prime }+y+2 x \right )^{2}-4 x y-4 x^{2}-4 a = 0 \]	✓	✓	✗

10437	\[ {} y^{\prime }-1 = 0 \]	✓	✓	✓

10438	\[ {} x^{2} {y^{\prime }}^{2}-2 x y y^{\prime }+y \left (y+1\right )-x = 0 \]	✓	✓	✓

10439	\[ {} x^{2} {y^{\prime }}^{2}-2 x y y^{\prime }+y^{2} \left (-x^{2}+1\right )-x^{4} = 0 \]	✓	✓	✗

10440	\[ {} x^{2} {y^{\prime }}^{2}-\left (2 x y+a \right ) y^{\prime }+y^{2} = 0 \]	✓	✓	✓

10441	\[ {} x^{2} {y^{\prime }}^{2}+3 x y y^{\prime }+2 y^{2} = 0 \]	✓	✓	✓

10442	\[ {} x^{2} {y^{\prime }}^{2}+3 x y y^{\prime }+3 y^{2} = 0 \]	✓	✓	✓

10443	\[ {} x^{2} {y^{\prime }}^{2}+4 x y y^{\prime }-5 y^{2} = 0 \]	✓	✓	✓

10444	\[ {} x^{2} {y^{\prime }}^{2}-4 x \left (y+2\right ) y^{\prime }+4 y \left (y+2\right ) = 0 \]	✓	✓	✓

10445	\[ {} x^{2} {y^{\prime }}^{2}+\left (x^{2} y-2 x y+x^{3}\right ) y^{\prime }+\left (y^{2}-x^{2} y\right ) \left (1-x \right ) = 0 \]	✓	✓	✓

10446	\[ {} x^{2} {y^{\prime }}^{2}-y \left (y-2 x \right ) y^{\prime }+y^{2} = 0 \]	✓	✓	✓

10447	\[ {} x^{2} {y^{\prime }}^{2}+\left (a \,x^{2} y^{3}+b \right ) y^{\prime }+a b y^{3} = 0 \]	✓	✓	✓

10448	\[ {} \left (x^{2}+1\right ) {y^{\prime }}^{2}-2 x y y^{\prime }+y^{2}-1 = 0 \]	✓	✓	✗

10449	\[ {} \left (x^{2}-1\right ) {y^{\prime }}^{2}-1 = 0 \]	✓	✓	✓

10450	\[ {} \left (x^{2}-1\right ) {y^{\prime }}^{2}-y^{2}+1 = 0 \]	✓	✓	✓

10451	\[ {} \left (-a^{2}+x^{2}\right ) {y^{\prime }}^{2}+2 x y y^{\prime }+y^{2} = 0 \]	✓	✓	✓

10452	\[ {} \left (-a^{2}+x^{2}\right ) {y^{\prime }}^{2}-2 x y y^{\prime }-x^{2} = 0 \]	✓	✓	✗

10453	\[ {} \left (x^{2}+a \right ) {y^{\prime }}^{2}-2 x y y^{\prime }+y^{2}+b = 0 \]	✓	✓	✗

10454	\[ {} \left (2 x^{2}+1\right ) {y^{\prime }}^{2}+\left (x^{2}+2 x y+y^{2}+2\right ) y^{\prime }+2 y^{2}+1 = 0 \]	✓	✗	✗

10455	\[ {} \left (a^{2}-1\right ) x^{2} {y^{\prime }}^{2}+2 x y y^{\prime }-y^{2}+a^{2} x^{2} = 0 \]	✓	✓	✓

10456	\[ {} a \,x^{2} {y^{\prime }}^{2}-2 a x y y^{\prime }+y^{2}-a \left (a -1\right ) x^{2} = 0 \]	✓	✓	✓

10457	\[ {} x^{3} {y^{\prime }}^{2}+x^{2} y y^{\prime }+a = 0 \]	✓	✓	✗

10458	\[ {} x \left (x^{2}-1\right ) {y^{\prime }}^{2}+2 \left (-x^{2}+1\right ) y y^{\prime }+x y^{2}-x = 0 \]	✓	✓	✗

10459	\[ {} x^{4} {y^{\prime }}^{2}-x y^{\prime }-y = 0 \]	✓	✓	✓

10460	\[ {} x^{2} \left (-a^{2}+x^{2}\right ) {y^{\prime }}^{2}-1 = 0 \]	✓	✓	✓

10461	\[ {} {\mathrm e}^{-2 x} {y^{\prime }}^{2}-\left (y^{\prime }-1\right )^{2}+{\mathrm e}^{-2 y} = 0 \]	✓	✓	✗

10462	\[ {} \left ({y^{\prime }}^{2}+y^{2}\right ) \cos \left (x \right )^{4}-a^{2} = 0 \]	✗	✗	✗

10463	\[ {} y {y^{\prime }}^{2}-1 = 0 \]	✓	✓	✓

10464	\[ {} y {y^{\prime }}^{2}-{\mathrm e}^{2 x} = 0 \]	✓	✓	✓

10465	\[ {} y {y^{\prime }}^{2}+2 x y^{\prime }-y = 0 \]	✓	✓	✗

10466	\[ {} y {y^{\prime }}^{2}+2 x y^{\prime }-9 y = 0 \]	✓	✓	✓

10467	\[ {} y {y^{\prime }}^{2}-2 x y^{\prime }+y = 0 \]	✓	✓	✗

10468	\[ {} y {y^{\prime }}^{2}-4 x y^{\prime }+y = 0 \]	✓	✓	✓

10469	\[ {} y {y^{\prime }}^{2}-4 a^{2} x y^{\prime }+a^{2} y = 0 \]	✓	✓	✓

10470	\[ {} y {y^{\prime }}^{2}+a x y^{\prime }+b y = 0 \]	✓	✓	✓

10471	\[ {} y {y^{\prime }}^{2}+x^{3} y^{\prime }-x^{2} y = 0 \]	✓	✓	✗

10472	\[ {} y {y^{\prime }}^{2}-\left (y-x \right ) y^{\prime }-x = 0 \]	✓	✓	✓

10473	\[ {} {y^{\prime }}^{2} \left (x +y\right )+2 x y^{\prime }-y = 0 \]	✓	✓	✓

10474	\[ {} \left (y-2 x \right ) {y^{\prime }}^{2}-2 \left (x -1\right ) y^{\prime }+y-2 = 0 \]	✓	✓	✗

10475	\[ {} 2 y {y^{\prime }}^{2}-\left (4 x -5\right ) y^{\prime }+2 y = 0 \]	✓	✓	✗

10476	\[ {} 4 y {y^{\prime }}^{2}+2 x y^{\prime }-y = 0 \]	✓	✓	✗

10477	\[ {} 9 y {y^{\prime }}^{2}+4 x^{3} y^{\prime }-4 x^{2} y = 0 \]	✓	✓	✗

10478	\[ {} a y {y^{\prime }}^{2}+\left (2 x -b \right ) y^{\prime }-y = 0 \]	✓	✓	✗

10479	\[ {} \left (a y+b \right ) \left (1+{y^{\prime }}^{2}\right )-c = 0 \]	✓	✓	✓

10480	\[ {} \left (b_{2} y+a_{2} x +c_{2} \right ) {y^{\prime }}^{2}+\left (a_{1} x +b_{1} y+c_{1} \right ) y^{\prime }+a_{0} x +b_{0} y+c_{0} = 0 \]	✓	✓	✗

10481	\[ {} \left (a y-x^{2}\right ) {y^{\prime }}^{2}+2 x y {y^{\prime }}^{2}-y^{2} = 0 \]	✗	✗	✗

10482	\[ {} x y {y^{\prime }}^{2}+\left (x^{2}+y^{2}\right ) y^{\prime }+x y = 0 \]	✓	✓	✓

10483	\[ {} x y {y^{\prime }}^{2}+\left (x^{22}-y^{2}+a \right ) y^{\prime }-x y = 0 \]	✗	✗	✗

10484	\[ {} \left (2 x y-x^{2}\right ) {y^{\prime }}^{2}+2 x y y^{\prime }+2 x y-y^{2} = 0 \]	✓	✓	✗

10485	\[ {} \left (2 x y-x^{2}\right ) {y^{\prime }}^{2}-6 x y y^{\prime }-y^{2}+2 x y = 0 \]	✓	✓	✓

10486	\[ {} a x y {y^{\prime }}^{2}-\left (y^{2} a +b \,x^{2}+c \right ) y^{\prime }+b x y = 0 \]	✓	✓	✗

10487	\[ {} y^{2} {y^{\prime }}^{2}+y^{2}-a^{2} = 0 \]	✓	✓	✓

10488	\[ {} y^{2} {y^{\prime }}^{2}-6 x^{3} y^{\prime }+4 x^{2} y = 0 \]	✓	✓	✗

10489	\[ {} y^{2} {y^{\prime }}^{2}-4 a y y^{\prime }+y^{2}-4 a x +4 a^{2} = 0 \]	✓	✓	✗

10490	\[ {} y^{2} {y^{\prime }}^{2}+2 x y y^{\prime }+y^{2} a +b x +c = 0 \]	✓	✓	✗

10491	\[ {} y^{2} {y^{\prime }}^{2}-2 x y y^{\prime }+2 y^{2}-x^{2}+a = 0 \]	✓	✓	✗

10492	\[ {} y^{2} {y^{\prime }}^{2}+2 a x y y^{\prime }+\left (-a +1\right ) y^{2}+a \,x^{2}+\left (a -1\right ) b = 0 \]	✓	✓	✗

10493	\[ {} \left (y^{2}-a^{2}\right ) {y^{\prime }}^{2}+y^{2} = 0 \]	✓	✓	✓

10494	\[ {} \left (y^{2}-2 a x +a^{2}\right ) {y^{\prime }}^{2}+2 a y y^{\prime }+y^{2} = 0 \]	✓	✓	✗

10495	\[ {} \left (y^{2}-a^{2} x^{2}\right ) {y^{\prime }}^{2}+2 x y y^{\prime }+\left (-a^{2}+1\right ) x^{2} = 0 \]	✓	✓	✗

10496	\[ {} \left (y^{2}+\left (-a +1\right ) x^{2}\right ) {y^{\prime }}^{2}+2 a x y y^{\prime }+\left (-a +1\right ) y^{2}+x^{2} = 0 \]	✓	✓	✗

10497	\[ {} \left (y-x \right )^{2} \left (1+{y^{\prime }}^{2}\right )-a^{2} \left (y^{\prime }+1\right )^{2} = 0 \]	✓	✓	✓

10498	\[ {} 3 y^{2} {y^{\prime }}^{2}-2 x y y^{\prime }+4 y^{2}-x^{2} = 0 \]	✓	✓	✗

10499	\[ {} \left (3 y-2\right ) {y^{\prime }}^{2}-4+4 y = 0 \]	✓	✓	✓

10500	\[ {} \left (-a^{2}+1\right ) y^{2} {y^{\prime }}^{2}-2 a^{2} x y y^{\prime }+y^{2}-a^{2} x^{2} = 0 \]	✓	✓	✗

6.105 Problems 10401 to 10500