4.88 Problems 8701 to 8800

Table 4.175: Main lookup table sequentially arranged

#

ODE

Mathematica

Maple

8701

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

8702

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

8703

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

8704

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

8705

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

8706

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

8707

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

8708

\[ {}{y^{\prime }}^{2}-4 y^{3}+a y+b = 0 \]

8709

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

8710

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

8711

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

8712

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

8713

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

8714

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

8715

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

8716

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

8717

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

8718

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

8719

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

8720

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

8721

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

8722

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

8723

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

8724

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

8725

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

8726

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

8727

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

8728

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

8729

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

8730

\[ {}{y^{\prime }}^{2}+2 f \left (x \right ) y y^{\prime }+g \left (x \right ) y^{2}-\left (g \left (x \right )-f \left (x \right )^{2}\right ) {\mathrm e}^{-2 \left (\int _{a}^{x}f \left (\operatorname {xp} \right )d \operatorname {xp} \right )} = 0 \]

8731

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

8732

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

8733

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

8734

\[ {}{y^{\prime }}^{2}-3 x y^{\frac {2}{3}} y^{\prime }+9 y^{\frac {5}{3}} = 0 \]

8735

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

8736

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

8737

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

8738

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

8739

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

8740

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

8741

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

8742

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

8743

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

8744

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

8745

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

8746

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

8747

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

8748

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

8749

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

8750

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

8751

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

8752

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

8753

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

8754

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

8755

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

8756

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

8757

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

8758

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

8759

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

8760

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

8761

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

8762

\[ {}\left (3 x +1\right ) {y^{\prime }}^{2}-3 \left (y+2\right ) y^{\prime }+9 = 0 \]

8763

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

8764

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

8765

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

8766

\[ {}\left (\operatorname {a2} x +\operatorname {c2} \right ) {y^{\prime }}^{2}+\left (\operatorname {a1} x +\operatorname {b1} y+\operatorname {c1} \right ) y^{\prime }+\operatorname {a0} x +\operatorname {b0} y+\operatorname {c0} = 0 \]

8767

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

8768

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

8769

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

8770

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

8771

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

8772

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

8773

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

8774

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

8775

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

8776

\[ {}x^{2} {y^{\prime }}^{2}+4 x y y^{\prime }-5 y^{2} = 0 \]

8777

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

8778

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

8779

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

8780

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

8781

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

8782

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

8783

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

8784

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

8785

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

8786

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

8787

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

8788

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

8789

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

8790

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

8791

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

8792

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

8793

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

8794

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

8795

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

8796

\[ {}\operatorname {d0} \left (x \right ) {y^{\prime }}^{2}+2 \operatorname {b0} \left (x \right ) y y^{\prime }+\operatorname {c0} \left (x \right ) y^{2}+2 \operatorname {d0} \left (x \right ) y^{\prime }+2 \operatorname {e0} \left (x \right ) y+\operatorname {f0} \left (x \right ) = 0 \]

8797

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

8798

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

8799

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

8800

\[ {}y {y^{\prime }}^{2}+2 x y^{\prime }-9 y = 0 \]