6.8 Problems 701 to 800

Table 6.15: Main lookup table sequentially arranged

#

ODE

Mathematica

Maple

Sympy

701

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

702

\[ {} y^{\prime } = 6 \,{\mathrm e}^{2 x -y} \]

703

\[ {} 2 \sqrt {x}\, y^{\prime } = \cos \left (y\right )^{2} \]

704

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

705

\[ {} -2 y+y^{\prime } = 3 \,{\mathrm e}^{2 x} \]

706

\[ {} 3 y+y^{\prime } = 2 x \,{\mathrm e}^{-3 x} \]

707

\[ {} -2 x y+y^{\prime } = {\mathrm e}^{x^{2}} \]

708

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

709

\[ {} 2 x y^{\prime }+y = 10 \sqrt {x} \]

710

\[ {} 2 x y^{\prime }+y = 10 \sqrt {x} \]

711

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

712

\[ {} x y^{\prime }-y = x \]

713

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

714

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

715

\[ {} 3 y+x y^{\prime } = 2 x^{5} \]

716

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

717

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

718

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

719

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

720

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

721

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

722

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

723

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

724

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

725

\[ {} y^{\prime } = 3 x^{2} {\mathrm e}^{x^{2}}+2 x y \]

726

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

727

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

728

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

729

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

730

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

731

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

732

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

733

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

734

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

735

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

736

\[ {} x^{2} y^{\prime } = {\mathrm e}^{\frac {y}{x}} x^{2}+x y \]

737

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

738

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

739

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

740

\[ {} x y y^{\prime } = y^{2}+x \sqrt {4 x^{2}+y^{2}} \]

741

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

742

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

743

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

744

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

745

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

746

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

747

\[ {} 2 x y+x^{2} y^{\prime } = 5 y^{3} \]

748

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

749

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

750

\[ {} 2 x y+x^{2} y^{\prime } = 5 y^{4} \]

751

\[ {} 6 y+x y^{\prime } = 3 x y^{{4}/{3}} \]

752

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

753

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

754

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

755

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

756

\[ {} x \,{\mathrm e}^{y} y^{\prime } = 2 \,{\mathrm e}^{y}+2 \,{\mathrm e}^{2 x} x^{3} \]

757

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

758

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

759

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

760

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

761

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

762

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

763

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

764

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

765

\[ {} \cos \left (x \right )+\ln \left (y\right )+\left (\frac {x}{y}+{\mathrm e}^{y}\right ) y^{\prime } = 0 \]

766

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

767

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

768

\[ {} {\mathrm e}^{x} \sin \left (y\right )+\tan \left (y\right )+\left ({\mathrm e}^{x} \cos \left (y\right )+x \sec \left (y\right )^{2}\right ) y^{\prime } = 0 \]

769

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

770

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

771

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

772

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

773

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

774

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

775

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

776

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

777

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

778

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

779

\[ {} 2 y+x y^{\prime } = 6 x^{2} \sqrt {y} \]

780

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

781

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

782

\[ {} 6 x y^{3}+2 y^{4}+\left (9 x^{2} y^{2}+8 x y^{3}\right ) y^{\prime } = 0 \]

783

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

784

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

785

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

786

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

787

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

788

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

789

\[ {} 3 x^{5} y^{2}+x^{3} y^{\prime } = 2 y^{2} \]

790

\[ {} 3 y+x y^{\prime } = \frac {3}{x^{{3}/{2}}} \]

791

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

792

\[ {} x y^{\prime } = 12 x^{4} y^{{2}/{3}}+6 y \]

793

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

794

\[ {} 9 x^{2} y^{2}+x^{{3}/{2}} y^{\prime } = y^{2} \]

795

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

796

\[ {} 9 \sqrt {x}\, y^{{4}/{3}}-12 x^{{1}/{5}} y^{{3}/{2}}+\left (8 x^{{3}/{2}} y^{{1}/{3}}-15 x^{{6}/{5}} \sqrt {y}\right ) y^{\prime } = 0 \]

797

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

798

\[ {} x y^{\prime }+y = 2 \,{\mathrm e}^{2 x} \]

799

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

800

\[ {} y^{\prime } = 3 x^{2} \left (7+y\right ) \]