4.14.7 Problems 601 to 700

Table 4.1135: First order ode non-linear in derivative

#

ODE

Mathematica

Maple

Sympy

10317

\[ {} {y^{\prime }}^{n} = 0 \]

10318

\[ {} x {y^{\prime }}^{n} = 0 \]

10319

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

10320

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

10321

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

10322

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

10323

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

10324

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

10325

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

10326

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

10327

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

10328

\[ {} {y^{\prime }}^{4} = \frac {1}{x y^{3}} \]

10329

\[ {} {y^{\prime }}^{2} = \frac {1}{y^{4} x^{3}} \]

11674

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

11675

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

11676

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

11677

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

11678

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

11679

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

11680

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

11681

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

11682

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

11683

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

11684

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

11685

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

11686

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

11687

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

11688

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

11689

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

11690

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

11691

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

11692

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

11693

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

11694

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

11695

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

11696

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

11697

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

11698

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

11699

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

11700

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

11701

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

11702

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

11703

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

11704

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

11705

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

11706

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

11707

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

11708

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

11709

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

11710

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

11711

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

11712

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

11713

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

11714

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

11715

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

11716

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

11717

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

11718

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

11719

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

11720

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

11721

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

11722

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

11723

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

11724

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

11725

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

11726

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

11727

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

11728

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

11729

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

11730

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

11731

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

11732

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

11733

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

11734

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

11735

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

11736

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

11738

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

11739

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

11740

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

11741

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

11742

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

11743

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

11744

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

11745

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

11746

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

11747

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

11748

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

11749

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

11750

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

11751

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

11752

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

11753

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

11754

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

11755

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

11756

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

11757

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

11758

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

11759

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

11760

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

11761

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