2.77 Problems 7601 to 7700

Table 2.77: Main lookup table

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ODE

Mathematica result

Maple result

7601

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

7602

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

7603

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

7604

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

7605

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

7606

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

7607

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

7608

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

7609

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

7610

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

7611

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

7612

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

7613

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

7614

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

7615

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

7616

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

7617

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

7618

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

7619

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

7620

\[ {}y^{\prime }-\mathit {a3} y^{3}-\mathit {a2} y^{2}-\mathit {a1} y-\mathit {a0} = 0 \]

7621

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

7622

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

7623

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

7624

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

7625

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

7626

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

7627

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

7628

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

7629

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

7630

\[ {}y^{\prime }+a \phi ^{\prime }\relax (x ) y^{3}+6 a \phi \relax (x ) y^{2}+\frac {\left (2 a +1\right ) y \phi ^{\prime \prime }\relax (x )}{\phi ^{\prime }\relax (x )}+2 a +2 = 0 \]

7631

\[ {}y^{\prime }-f_{3} \relax (x ) y^{3}-f_{2}\relax (x ) y^{2}-f_{1}\relax (x ) y-f_{0} \relax (x ) = 0 \]

7632

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

7633

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

7634

\[ {}y^{\prime }-f \relax (x )^{-n +1} g^{\prime }\relax (x ) y^{n} \left (a g \relax (x )+b \right )^{-n}-\frac {f^{\prime }\relax (x ) y}{f \relax (x )}-f \relax (x ) g^{\prime }\relax (x ) = 0 \]

7635

\[ {}y^{\prime }-a^{n} f \relax (x )^{-n +1} g^{\prime }\relax (x ) y^{n}-\frac {f^{\prime }\relax (x ) y}{f \relax (x )}-f \relax (x ) g^{\prime }\relax (x ) = 0 \]

7636

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

7637

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

7638

\[ {}y^{\prime }-\sqrt {{| y|}} = 0 \]

7639

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

7640

\[ {}y^{\prime }-a \sqrt {1+y^{2}}-b = 0 \]

7641

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

7642

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

7643

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

7644

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

7645

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

7646

\[ {}y^{\prime }-\sqrt {\frac {y^{3}+1}{x^{3}+1}} = 0 \]

7647

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

7648

\[ {}y^{\prime }-\frac {\sqrt {1-y^{4}}}{\sqrt {-x^{4}+1}} = 0 \]

7649

\[ {}y^{\prime }-\sqrt {\frac {a y^{4}+b y^{2}+1}{a \,x^{4}+b \,x^{2}+1}} = 0 \]

7650

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

7651

\[ {}y^{\prime }-\sqrt {\frac {a_{4} x^{4}+a_{3} x^{3}+a_{2} x^{2}+a_{1} x +a_{0}}{b_{4} y^{4}+b_{3} y^{3}+b_{2} y^{2}+b_{1} y+b_{0}}} = 0 \]

7652

\[ {}y^{\prime }-\sqrt {\frac {b_{4} y^{4}+b_{3} y^{3}+b_{2} y^{2}+b_{1} y+b_{0}}{a_{4} x^{4}+a_{3} x^{3}+a_{2} x^{2}+a_{1} x +a_{0}}} = 0 \]

7653

\[ {}y^{\prime }-\mathit {R1} \left (x , \sqrt {a_{4} x^{4}+a_{3} x^{3}+a_{2} x^{2}+a_{1} x +a_{0}}\right ) \mathit {R2} \left (y, \sqrt {b_{4} y^{4}+b_{3} y^{3}+b_{2} y^{2}+b_{1} y+b_{0}}\right ) = 0 \]

7654

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

7655

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

7656

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

7657

\[ {}y^{\prime }-a \cos \relax (y)+b = 0 \]

7658

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

7659

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

7660

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

7661

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

7662

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

7663

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

7664

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

7665

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

7666

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

7667

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

7668

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

7669

\[ {}2 y^{\prime }-3 y^{2}-4 a y-b -c \,{\mathrm e}^{-2 a x} = 0 \]

7670

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

7671

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

7672

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

7673

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

7674

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

7675

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

7676

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

7677

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

7678

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

7679

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

7680

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

7681

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

7682

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

7683

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

7684

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

7685

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

7686

\[ {}x y^{\prime }+a x y^{2}+b y+c x +d = 0 \]

7687

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

7688

\[ {}x y^{\prime }+a \,x^{\alpha } y^{2}+b y-c \,x^{\beta } = 0 \]

7689

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

7690

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

7691

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

7692

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

7693

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

7694

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

7695

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

7696

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

7697

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

7698

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

7699

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

7700

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