2.78 Problems 7701 to 7800

Table 2.78: Main lookup table

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ODE

Mathematica result

Maple result

7701

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

7702

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

7703

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

7704

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

7705

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

7706

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

7707

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

7708

\[ {}x y^{\prime }+a y-f \relax (x ) g \left (x^{a} y\right ) = 0 \]

7709

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

7710

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

7711

\[ {}\left (1+2 x \right ) y^{\prime }-4 \,{\mathrm e}^{-y}+2 = 0 \]

7712

\[ {}3 x y^{\prime }-3 x \ln \relax (x ) y^{4}-y = 0 \]

7713

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

7714

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

7715

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

7716

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

7717

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

7718

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

7719

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

7720

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

7721

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

7722

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

7723

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

7724

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

7725

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

7726

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

7727

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

7728

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

7729

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

7730

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

7731

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

7732

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

7733

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

7734

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

7735

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

7736

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

7737

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

7738

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

7739

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

7740

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

7741

\[ {}\left (x^{2}-5 x +6\right ) y^{\prime }+3 x y-8 y+x^{2} = 0 \]

7742

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

7743

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

7744

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

7745

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

7746

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

7747

\[ {}3 x^{2} y^{\prime }-7 y^{2}-3 x y-x^{2} = 0 \]

7748

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

7749

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

7750

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

7751

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

7752

\[ {}x^{3} y^{\prime }-x^{4} y^{2}+x^{2} y+20 = 0 \]

7753

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

7754

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

7755

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

7756

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

7757

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

7758

\[ {}2 x \left (x^{2}-1\right ) y^{\prime }+2 \left (x^{2}-1\right ) y^{2}-\left (3 x^{2}-5\right ) y+x^{2}-3 = 0 \]

7759

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

7760

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

7761

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

7762

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

7763

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

7764

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

7765

\[ {}x^{7} y^{\prime }+2 \left (x^{2}+1\right ) y^{3}+5 x^{3} y^{2} = 0 \]

7766

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

7767

\[ {}x^{n} y^{\prime }-a y^{2}-b \,x^{2 n -2} = 0 \]

7768

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

7769

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

7770

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

7771

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

7772

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

7773

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

7774

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

7775

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

7776

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

7777

\[ {}\cos \relax (x ) y^{\prime }-y^{4}-y \sin \relax (x ) = 0 \]

7778

\[ {}\sin \relax (x ) \cos \relax (x ) y^{\prime }-y-\left (\sin ^{3}\relax (x )\right ) = 0 \]

7779

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

7780

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

7781

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

7782

\[ {}f \relax (x ) y^{\prime }+g \relax (x ) s \relax (y)+h \relax (x ) = 0 \]

7783

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

7784

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

7785

\[ {}y y^{\prime }+a y+\frac {\left (a^{2}-1\right ) x}{4}+b \,x^{n} = 0 \]

7786

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

7787

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

7788

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

7789

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

7790

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

7791

\[ {}y y^{\prime }-x \,{\mathrm e}^{\frac {x}{y}} = 0 \]

7792

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

7793

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

7794

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

7795

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

7796

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

7797

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

7798

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

7799

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

7800

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