4.28 Problems 2701 to 2800

Table 4.55: Main lookup table sequentially arranged

#

ODE

Mathematica

Maple

2701

\[ {}y^{\prime } = \left (9 x -y\right )^{2} \]

2702

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

2703

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

2704

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

2705

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

2706

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

2707

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

2708

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

2709

\[ {}y^{\prime }+\frac {7 y}{x}-3 y^{2} = \frac {3}{x^{2}} \]

2710

\[ {}\frac {y^{\prime }}{y}+p \left (x \right ) \ln \left (y\right ) = q \left (x \right ) \]

2711

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

2712

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

2713

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

2714

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

2715

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

2716

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

2717

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

2718

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

2719

\[ {}4 \,{\mathrm e}^{2 x}+2 x y-y^{2}+\left (x -y\right )^{2} y^{\prime } = 0 \]

2720

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

2721

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

2722

\[ {}2 y^{2} {\mathrm e}^{2 x}+3 x^{2}+2 y \,{\mathrm e}^{2 x} y^{\prime } = 0 \]

2723

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

2724

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

2725

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

2726

\[ {}y^{\prime \prime }+7 y^{\prime }+10 y = 0 \]

2727

\[ {}y^{\prime \prime }-36 y = 0 \]

2728

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

2729

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

2730

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

2731

\[ {}y^{\prime \prime \prime }+3 y^{\prime \prime }-18 y^{\prime }-40 y = 0 \]

2732

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

2733

\[ {}y^{\prime \prime \prime }+y^{\prime \prime }-10 y^{\prime }+8 y = 0 \]

2734

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

2735

\[ {}y^{\prime \prime \prime \prime }-13 y^{\prime \prime }+36 y = 0 \]

2736

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

2737

\[ {}2 x^{2} y^{\prime \prime }+5 x y^{\prime }+y = 0 \]

2738

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

2739

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

2740

\[ {}y^{\prime \prime }+y^{\prime }-6 y = 18 \,{\mathrm e}^{5 x} \]

2741

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

2742

\[ {}y^{\prime \prime \prime }+2 y^{\prime \prime }-y^{\prime }-2 y = 4 \,{\mathrm e}^{2 x} \]

2743

\[ {}y^{\prime \prime \prime }+y^{\prime \prime }-10 y^{\prime }+8 y = 24 \,{\mathrm e}^{-3 x} \]

2744

\[ {}y^{\prime \prime \prime }+5 y^{\prime \prime }+6 y^{\prime } = 6 \,{\mathrm e}^{-x} \]

2745

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

2746

\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = 5 \,{\mathrm e}^{-2 x} x \]

2747

\[ {}y^{\prime \prime }+4 y = 8 \sin \left (2 x \right ) \]

2748

\[ {}y^{\prime \prime }-y^{\prime }-2 y = 5 \,{\mathrm e}^{2 x} \]

2749

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

2750

\[ {}y^{\prime \prime \prime }+2 y^{\prime \prime }-5 y^{\prime }-6 y = 4 x^{2} \]

2751

\[ {}y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = 9 \,{\mathrm e}^{-x} \]

2752

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

2753

\[ {}y^{\prime \prime }+9 y = 5 \cos \left (2 x \right ) \]

2754

\[ {}y^{\prime \prime }-y = 9 \,{\mathrm e}^{2 x} x \]

2755

\[ {}y^{\prime \prime }+y^{\prime }-2 y = -10 \sin \left (x \right ) \]

2756

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

2757

\[ {}y^{\prime \prime }+\omega ^{2} y = \frac {F_{0} \cos \left (\omega t \right )}{m} \]

2758

\[ {}y^{\prime \prime }-4 y^{\prime }+6 y = 7 \,{\mathrm e}^{2 x} \]

2759

\[ {}y^{\prime \prime \prime }+y^{\prime \prime }+y^{\prime }+y = 4 x \,{\mathrm e}^{x} \]

2760

\[ {}y^{\prime \prime \prime \prime }+104 y^{\prime \prime \prime }+2740 y^{\prime \prime } = 5 \,{\mathrm e}^{-2 x} \cos \left (3 x \right ) \]

2761

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

2762

\[ {}y^{\prime \prime }+6 y = \sin \left (x \right )^{2} \cos \left (x \right )^{2} \]

2763

\[ {}y^{\prime \prime }-16 y = 20 \cos \left (4 x \right ) \]

2764

\[ {}y^{\prime \prime }+2 y^{\prime }+y = 50 \sin \left (3 x \right ) \]

2765

\[ {}y^{\prime \prime }-y = 10 \,{\mathrm e}^{2 x} \cos \left (x \right ) \]

2766

\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = 169 \sin \left (3 x \right ) \]

2767

\[ {}y^{\prime \prime }-y^{\prime }-2 y = 40 \sin \left (x \right )^{2} \]

2768

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

2769

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

2770

\[ {}y^{\prime \prime }-4 y = 100 \,{\mathrm e}^{x} \sin \left (x \right ) x \]

2771

\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 4 \,{\mathrm e}^{-x} \cos \left (2 x \right ) \]

2772

\[ {}y^{\prime \prime }-2 y^{\prime }+10 y = 24 \,{\mathrm e}^{x} \cos \left (3 x \right ) \]

2773

\[ {}y^{\prime \prime }+16 y = 34 \,{\mathrm e}^{x}+16 \cos \left (4 x \right )-8 \sin \left (4 x \right ) \]

2774

\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = 4 \,{\mathrm e}^{3 x} \ln \left (x \right ) \]

2775

\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = \frac {{\mathrm e}^{-2 x}}{x^{2}} \]

2776

\[ {}y^{\prime \prime }+9 y = 18 \sec \left (3 x \right )^{3} \]

2777

\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = \frac {2 \,{\mathrm e}^{-3 x}}{x^{2}+1} \]

2778

\[ {}y^{\prime \prime }-4 y = \frac {8}{{\mathrm e}^{2 x}+1} \]

2779

\[ {}y^{\prime \prime }-4 y^{\prime }+5 y = {\mathrm e}^{2 x} \tan \left (x \right ) \]

2780

\[ {}y^{\prime \prime }+9 y = \frac {36}{4-\cos \left (3 x \right )^{2}} \]

2781

\[ {}y^{\prime \prime }-10 y^{\prime }+25 y = \frac {2 \,{\mathrm e}^{5 x}}{x^{2}+4} \]

2782

\[ {}y^{\prime \prime }-6 y^{\prime }+13 y = 4 \,{\mathrm e}^{3 x} \sec \left (2 x \right )^{2} \]

2783

\[ {}y^{\prime \prime }+y = \sec \left (x \right )+4 \,{\mathrm e}^{x} \]

2784

\[ {}y^{\prime \prime }+y = \csc \left (x \right )+2 x^{2}+5 x +1 \]

2785

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

2786

\[ {}y^{\prime \prime }-2 m y^{\prime }+m^{2} y = \frac {{\mathrm e}^{m x}}{x^{2}+1} \]

2787

\[ {}y^{\prime \prime }-2 y^{\prime }+y = \frac {4 \,{\mathrm e}^{x} \ln \left (x \right )}{x^{3}} \]

2788

\[ {}y^{\prime \prime }+2 y^{\prime }+y = \frac {{\mathrm e}^{-x}}{\sqrt {-x^{2}+4}} \]

2789

\[ {}y^{\prime \prime }+2 y^{\prime }+17 y = \frac {64 \,{\mathrm e}^{-x}}{3+\sin \left (4 x \right )^{2}} \]

2790

\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = \frac {4 \,{\mathrm e}^{-2 x}}{x^{2}+1}+2 x^{2}-1 \]

2791

\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = 15 \,{\mathrm e}^{-2 x} \ln \left (x \right )+25 \cos \left (x \right ) \]

2792

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

2793

\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y = 36 \,{\mathrm e}^{2 x} \ln \left (x \right ) \]

2794

\[ {}y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y = \frac {2 \,{\mathrm e}^{-x}}{x^{2}+1} \]

2795

\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+9 y^{\prime } = 12 \,{\mathrm e}^{3 x} \]

2796

\[ {}y^{\prime \prime }-9 y = F \left (x \right ) \]

2797

\[ {}y^{\prime \prime }+5 y^{\prime }+4 y = F \left (x \right ) \]

2798

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

2799

\[ {}y^{\prime \prime }+4 y^{\prime }-12 y = F \left (x \right ) \]

2800

\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = 5 \,{\mathrm e}^{2 x} x \]