4.9.81 Problems 8001 to 8100

Table 4.999: First order ode linear in derivative

#

ODE

Mathematica

Maple

Sympy

22555

\[ {} i^{\prime } = \frac {t -i t}{t^{2}+1} \]

22556

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

22557

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

22558

\[ {} y^{\prime } = \frac {3 y^{2} \cot \left (x \right )+\cos \left (x \right ) \sin \left (x \right )}{2 y} \]

22559

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

22560

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

22561

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

22562

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

22563

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

22564

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

22565

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

22566

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

22567

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

22568

\[ {} i^{\prime }+3 i = {\mathrm e}^{-2 t} \]

22569

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

22570

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

22571

\[ {} r^{\prime } = t -\frac {r}{3 t} \]

22572

\[ {} i^{\prime }+2 i = 10 \,{\mathrm e}^{-2 t} \]

22573

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

22574

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

22576

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

22577

\[ {} x y^{\prime }+3 = 4 x \,{\mathrm e}^{-y} \]

22578

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

22579

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

22580

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

22581

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

22582

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

22583

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

22584

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

22585

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

22586

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

22587

\[ {} y-y^{4} x^{5}+\left (x -x^{4} y^{5}\right ) y^{\prime } = 0 \]

22588

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

22589

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

22590

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

22591

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

22592

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

22621

\[ {} y^{\prime } = 3 y^{{2}/{3}} \]

22622

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

22624

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

22625

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

22626

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

22627

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

22628

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

22629

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

22630

\[ {} s^{2} t s^{\prime }+t^{2}+4 = 0 \]

22631

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

22632

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

22633

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

22634

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

22635

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

22636

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

22637

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

22638

\[ {} r^{2} \sin \left (t \right ) = \left (2 r \cos \left (t \right )+10\right ) r^{\prime } \]

22639

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

22640

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

22641

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

22642

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

22643

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

22644

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

22645

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

22646

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

22647

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

22648

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

22649

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

22650

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

22651

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

22652

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

22653

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

22654

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

22655

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

22656

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

22657

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

22659

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

22660

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

22661

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

22662

\[ {} s^{\prime } = \sqrt {\frac {1-t}{1-s}} \]

22663

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

22664

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

22665

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

22666

\[ {} n^{\prime } = -a n \]

22667

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

22668

\[ {} i^{\prime }+i = {\mathrm e}^{t} \]

22669

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

22670

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

22671

\[ {} q^{\prime } = \frac {p \,{\mathrm e}^{p^{2}-q^{2}}}{q} \]

22672

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

22673

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

22674

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

22675

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

22676

\[ {} r^{\prime } = \frac {r \left (1+\ln \left (t \right )\right )}{t \left (1+\ln \left (r\right )\right )} \]

22677

\[ {} u^{\prime } = -a \left (u-100 t \right ) \]

22678

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

22679

\[ {} i^{\prime }+3 i = 10 \sin \left (t \right ) \]

22680

\[ {} s^{\prime } = \frac {1}{s+t +1} \]

22682

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

22683

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

22684

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

22685

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

22686

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