6.78 Problems 7701 to 7800

Table 6.155: Main lookup table sequentially arranged

#

ODE

Mathematica

Maple

Sympy

7701

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

7702

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

7703

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

7704

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

7705

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

7706

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

7707

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

7708

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

7709

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

7710

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

7711

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

7712

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

7713

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

7714

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

7715

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

7716

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

7717

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

7718

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

7719

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

7720

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

7721

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

7722

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

7723

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

7724

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

7725

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

7726

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

7727

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

7728

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

7729

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

7730

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

7731

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

7732

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

7733

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

7734

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

7735

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

7736

\[ {} 3 y-7 x +7+\left (7 y-3 x +3\right ) y^{\prime } = 0 \]

7737

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

7738

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

7739

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

7740

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

7741

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

7742

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

7743

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

7744

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

7745

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

7746

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

7747

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

7748

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

7749

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

7750

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

7751

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

7752

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

7753

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

7754

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

7755

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

7756

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

7757

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

7758

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

7759

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

7760

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

7761

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

7762

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

7763

\[ {} \frac {r \tan \left (\theta \right ) r^{\prime }}{a^{2}-r^{2}} = 1 \]

7764

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

7765

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

7766

\[ {} y^{\prime \prime }-y^{\prime }-2 y = 8 \]

7767

\[ {} y^{\prime \prime }-4 y = 10 \,{\mathrm e}^{3 x} \]

7768

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

7769

\[ {} y^{\prime \prime }+25 y = 5 x^{2}+x \]

7770

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

7771

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

7772

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

7773

\[ {} y^{\prime \prime }-6 y^{\prime }+8 y = 8 \,{\mathrm e}^{4 x} \]

7774

\[ {} 2 y^{\prime \prime }-7 y^{\prime }-4 y = {\mathrm e}^{3 x} \]

7775

\[ {} y^{\prime \prime }-6 y^{\prime }+9 y = 54 x +18 \]

7776

\[ {} 6 y-5 y^{\prime }+y^{\prime \prime } = 100 \sin \left (4 x \right ) \]

7777

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

7778

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

7779

\[ {} y^{\prime \prime }-y^{\prime }+10 y = 20-{\mathrm e}^{2 x} \]

7780

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

7781

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

7782

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

7783

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

7784

\[ {} x^{\prime \prime }+4 x^{\prime }+3 x = {\mathrm e}^{-3 t} \]

7785

\[ {} y^{\prime \prime }+4 y^{\prime }+5 y = 6 \sin \left (t \right ) \]

7786

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

7787

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

7788

\[ {} y^{\prime \prime }+6 y^{\prime }+10 y = 50 x \]

7789

\[ {} x^{\prime \prime }+2 x^{\prime }+2 x = 85 \sin \left (3 t \right ) \]

7790

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

7791

\[ {} \frac {x^{\prime \prime }}{2} = -48 x \]

7792

\[ {} x^{\prime \prime }+5 x^{\prime }+6 x = \cos \left (t \right ) \]

7793

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

7794

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

7795

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

7796

\[ {} y^{\prime \prime }-6 y^{\prime }+25 y = 2 \sin \left (\frac {t}{2}\right )-\cos \left (\frac {t}{2}\right ) \]

7797

\[ {} y^{\prime \prime }-6 y^{\prime }+25 y = 64 \,{\mathrm e}^{-t} \]

7798

\[ {} y^{\prime \prime }-6 y^{\prime }+25 y = 50 t^{3}-36 t^{2}-63 t +18 \]

7799

\[ {} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y = 2 x \,{\mathrm e}^{-x} \]

7800

\[ {} y^{\prime \prime } = 9 x^{2}+2 x -1 \]