5.1.3 Problems 201 to 300

Table 5.5: First order ode

#

ODE

Mathematica

Maple

654

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

655

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

656

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

657

\[ {}y^{\prime } = \frac {10}{x^{2}+1} \]

658

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

659

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

660

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

661

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

662

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

663

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

664

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

665

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

666

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

667

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

668

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

669

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

670

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

671

\[ {}y^{\prime } = y^{{1}/{3}} \]

672

\[ {}y^{\prime } = y^{{1}/{3}} \]

673

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

674

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

675

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

676

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

677

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

678

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

679

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

680

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

681

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

682

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

683

\[ {}y^{\prime } = 4 \left (x y\right )^{{1}/{3}} \]

684

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

685

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

686

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

687

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

688

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

689

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

690

\[ {}y^{\prime } = \frac {\left (x -1\right ) y^{5}}{x^{2} \left (2 y^{3}-y\right )} \]

691

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

692

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

693

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

694

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

695

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

696

\[ {}2 y y^{\prime } = \frac {x}{\sqrt {x^{2}-16}} \]

697

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

698

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

699

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

700

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

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

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

705

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

706

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

707

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

708

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

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

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

714

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

715

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

716

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

717

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

718

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

719

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

720

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

721

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

722

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

723

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

724

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

725

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

726

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

727

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

728

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

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

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

736

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

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

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

743

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

744

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

745

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

746

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

747

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

748

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

749

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

750

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

751

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

752

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

753

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