6.57 Problems 5601 to 5700

Table 6.113: Main lookup table sequentially arranged

#

ODE

Mathematica

Maple

Sympy

5601

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

5602

\[ {} x y^{2} {y^{\prime }}^{2}-y^{3} y^{\prime }+a^{2} x = 0 \]

5603

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

5604

\[ {} 2 x y^{2} {y^{\prime }}^{2}-y^{3} y^{\prime }-a = 0 \]

5605

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

5606

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

5607

\[ {} 3 x y^{4} {y^{\prime }}^{2}-y^{5} y^{\prime }+1 = 0 \]

5608

\[ {} 9 x y^{4} {y^{\prime }}^{2}-3 y^{5} y^{\prime }-a = 0 \]

5609

\[ {} 9 \left (-x^{2}+1\right ) y^{4} {y^{\prime }}^{2}+6 x y^{5} y^{\prime }+4 x^{2} = 0 \]

5610

\[ {} {y^{\prime }}^{3} = b x +a \]

5611

\[ {} {y^{\prime }}^{3} = a \,x^{n} \]

5612

\[ {} {y^{\prime }}^{3}+x -y = 0 \]

5613

\[ {} {y^{\prime }}^{3} = \left (a +b y+c y^{2}\right ) f \left (x \right ) \]

5614

\[ {} {y^{\prime }}^{3} = \left (y-a \right )^{2} \left (y-b \right )^{2} \]

5615

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

5616

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

5617

\[ {} {y^{\prime }}^{3}+y^{\prime }+a -b x = 0 \]

5618

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

5619

\[ {} {y^{\prime }}^{3}+y^{\prime } = {\mathrm e}^{y} \]

5620

\[ {} {y^{\prime }}^{3}-7 y^{\prime }+6 = 0 \]

5621

\[ {} {y^{\prime }}^{3}-x y^{\prime }+a y = 0 \]

5622

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

5623

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

5624

\[ {} {y^{\prime }}^{3}-a x y^{\prime }+x^{3} = 0 \]

5625

\[ {} {y^{\prime }}^{3}+a x y^{\prime }-a y = 0 \]

5626

\[ {} {y^{\prime }}^{3}-\left (b x +a \right ) y^{\prime }+b y = 0 \]

5627

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

5628

\[ {} {y^{\prime }}^{3}-a x y y^{\prime }+2 a y^{2} = 0 \]

5629

\[ {} {y^{\prime }}^{3}-y^{4} y^{\prime } x -y^{5} = 0 \]

5630

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

5631

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

5632

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

5633

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

5634

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

5635

\[ {} {y^{\prime }}^{3}-a {y^{\prime }}^{2}+b y+a b x = 0 \]

5636

\[ {} {y^{\prime }}^{3}+a_{0} {y^{\prime }}^{2}+a_{1} y^{\prime }+a_{2} +a_{3} y = 0 \]

5637

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

5638

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

5639

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

5640

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

5641

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

5642

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

5643

\[ {} {y^{\prime }}^{3}-\left (x^{2}+x y^{2}+y^{4}\right ) {y^{\prime }}^{2}+x y^{2} \left (x^{2}+x y^{2}+y^{4}\right ) y^{\prime }-x^{3} y^{6} = 0 \]

5644

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

5645

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

5646

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

5647

\[ {} 4 {y^{\prime }}^{3}+4 y^{\prime } = x \]

5648

\[ {} 8 {y^{\prime }}^{3}+12 {y^{\prime }}^{2} = 27 x +27 y \]

5649

\[ {} x {y^{\prime }}^{3}-y {y^{\prime }}^{2}+a = 0 \]

5650

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

5651

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

5652

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

5653

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

5654

\[ {} 8 x {y^{\prime }}^{3}-12 y {y^{\prime }}^{2}+9 y = 0 \]

5655

\[ {} x^{2} {y^{\prime }}^{3}-2 x y {y^{\prime }}^{2}+y^{2} y^{\prime }+1 = 0 \]

5656

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

5657

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

5658

\[ {} 2 {y^{\prime }}^{3} x^{3}+6 y {y^{\prime }}^{2} x^{2}-\left (1-6 x y\right ) y y^{\prime }+2 y^{3} = 0 \]

5659

\[ {} {y^{\prime }}^{3} x^{4}-y {y^{\prime }}^{2} x^{3}-x^{2} y^{2} y^{\prime }+x y^{3} = 1 \]

5660

\[ {} x^{6} {y^{\prime }}^{3}-x y^{\prime }-y = 0 \]

5661

\[ {} {y^{\prime }}^{3} y-3 x y^{\prime }+3 y = 0 \]

5662

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

5663

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

5664

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

5665

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

5666

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

5667

\[ {} 16 y^{2} {y^{\prime }}^{3}+2 x y^{\prime }-y = 0 \]

5668

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

5669

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

5670

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

5671

\[ {} {y^{\prime }}^{4} = \left (y-a \right )^{3} \left (y-b \right )^{2} \]

5672

\[ {} {y^{\prime }}^{4}+f \left (x \right ) \left (y-a \right )^{3} \left (y-b \right )^{2} = 0 \]

5673

\[ {} {y^{\prime }}^{4}+f \left (x \right ) \left (y-a \right )^{3} \left (y-b \right )^{3} = 0 \]

5674

\[ {} {y^{\prime }}^{4}+f \left (x \right ) \left (y-a \right )^{3} \left (y-b \right )^{3} \left (y-c \right )^{2} = 0 \]

5675

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

5676

\[ {} {y^{\prime }}^{4}-4 y {y^{\prime }}^{2} x^{2}+16 x y^{2} y^{\prime }-16 y^{3} = 0 \]

5677

\[ {} {y^{\prime }}^{4}+4 {y^{\prime }}^{3} y+6 y^{2} {y^{\prime }}^{2}-\left (1-4 y^{3}\right ) y^{\prime }-\left (3-y^{3}\right ) y = 0 \]

5678

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

5679

\[ {} {y^{\prime }}^{4} x -2 {y^{\prime }}^{3} y+12 x^{3} = 0 \]

5680

\[ {} 3 {y^{\prime }}^{5}-y y^{\prime }+1 = 0 \]

5681

\[ {} {y^{\prime }}^{6} = \left (y-a \right )^{4} \left (y-b \right )^{3} \]

5682

\[ {} {y^{\prime }}^{6}+f \left (x \right ) \left (y-a \right )^{4} \left (y-b \right )^{3} = 0 \]

5683

\[ {} {y^{\prime }}^{6}+f \left (x \right ) \left (y-a \right )^{5} \left (y-b \right )^{3} = 0 \]

5684

\[ {} {y^{\prime }}^{6}+f \left (x \right ) \left (y-a \right )^{5} \left (y-b \right )^{4} = 0 \]

5685

\[ {} x^{2} \left ({y^{\prime }}^{6}+3 y^{4}+3 y^{2}+1\right ) = a^{2} \]

5686

\[ {} 2 \sqrt {a y^{\prime }}+x y^{\prime }-y = 0 \]

5687

\[ {} \left (x -y\right ) \sqrt {y^{\prime }} = a \left (1+y^{\prime }\right ) \]

5688

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

5689

\[ {} \sqrt {1+{y^{\prime }}^{2}}+a y^{\prime } = x \]

5690

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

5691

\[ {} \sqrt {1+{y^{\prime }}^{2}} = x y^{\prime } \]

5692

\[ {} \sqrt {a^{2}+b^{2} {y^{\prime }}^{2}}+x y^{\prime }-y = 0 \]

5693

\[ {} a \sqrt {1+{y^{\prime }}^{2}}+x y^{\prime }-y = 0 \]

5694

\[ {} a x \sqrt {1+{y^{\prime }}^{2}}+x y^{\prime }-y = 0 \]

5695

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

5696

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

5697

\[ {} \cos \left (y^{\prime }\right )+x y^{\prime } = y \]

5698

\[ {} a \cos \left (y^{\prime }\right )+b y^{\prime }+x = 0 \]

5699

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

5700

\[ {} y^{\prime } \sin \left (y^{\prime }\right )+\cos \left (y^{\prime }\right ) = y \]