5.3.65 Problems 6401 to 6500

Table 5.175: Problems not solved by Sympy

#

ODE

Mathematica

Maple

Sympy

20518

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

20520

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

20521

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

20523

\[ {} y = \ln \left (\cos \left (y^{\prime }\right )\right )+y^{\prime } \tan \left (y^{\prime }\right ) \]

20524

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

20525

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

20530

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

20531

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

20533

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

20534

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

20535

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

20536

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

20537

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

20538

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

20544

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

20546

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

20547

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

20548

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

20549

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

20552

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

20554

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

20555

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

20557

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

20559

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

20562

\[ {} \left (1-3 x^{2} y+6 y^{2}\right ) y^{\prime } = 3 x y^{2}-x^{2} \]

20563

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

20565

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

20566

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

20567

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

20569

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

20573

\[ {} \left (8 {y^{\prime }}^{3}-27\right ) x = \frac {12 {y^{\prime }}^{2}}{x} \]

20574

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

20582

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

20583

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

20584

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

20586

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

20587

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

20588

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

20589

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

20590

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

20591

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

20592

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

20593

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

20594

\[ {} 8 x {y^{\prime }}^{3} = y \left (12 {y^{\prime }}^{2}-9\right ) \]

20596

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

20599

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

20630

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

20632

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

20633

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

20634

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

20636

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

20637

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

20638

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

20639

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

20640

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

20641

\[ {} \left (2 x^{2}+3 x \right ) y^{\prime \prime }+\left (6 x +3\right ) y^{\prime }+2 y = {\mathrm e}^{x} \left (1+x \right ) \]

20642

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

20643

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

20644

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

20645

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

20646

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

20647

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

20648

\[ {} x^{5} y^{\prime \prime }+3 x^{3} y^{\prime }+\left (3-6 x \right ) x^{2} y = x^{4}+2 x -5 \]

20650

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

20662

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

20663

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

20664

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

20666

\[ {} y^{\prime \prime } = \sqrt {1+{y^{\prime }}^{2}} \]

20670

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

20674

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

20677

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

20678

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

20679

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

20680

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

20683

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

20684

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

20687

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

20696

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

20697

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

20698

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

20699

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

20700

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

20701

\[ {} x^{2} y^{\prime \prime } = \sqrt {m \,x^{2} {y^{\prime }}^{3}+n y^{2}} \]

20702

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

20703

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

20704

\[ {} x^{2} y^{\prime \prime }+4 y^{2}-6 y = x^{4} {y^{\prime }}^{2} \]

20710

\[ {} y^{\prime \prime } = \frac {1}{\sqrt {a y}} \]

20711

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

20712

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

20716

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

20717

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

20718

\[ {} \left (x^{3}-4 x \right ) y^{\prime \prime \prime }+\left (9 x^{2}-4\right ) y^{\prime \prime }+18 x y^{\prime }+6 y = 6 \]

20719

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

20720

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

20721

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

20722

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

20723

\[ {} \left (3-x \right ) y^{\prime \prime }-\left (9-4 x \right ) y^{\prime }+\left (6-3 x \right ) y = 0 \]

20724

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

20725

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

20727

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