3.9.49 Problems 4801 to 4900

Table 3.603: First order ode linear in derivative

#

ODE

Mathematica

Maple

12575

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

12579

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

12580

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

12581

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

12582

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

12583

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

12585

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

12586

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

12590

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

12597

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

12598

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

12600

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

12602

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

12603

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

12615

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

12616

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

12617

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

12618

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

12619

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

12620

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

12621

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

12622

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

12623

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

12624

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

12625

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

12626

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

12627

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

12628

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

12629

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

12630

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

12631

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

12632

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

12633

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

12634

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

12635

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

12636

\[ {}y^{\prime } = \frac {1}{\sqrt {15-x^{2}-y^{2}}} \]

12637

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

12638

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

12639

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

12640

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

12641

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

12642

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

12643

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

12644

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

12645

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

12646

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

12647

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

12648

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

12649

\[ {}y^{\prime } = 4 y-5 \]

12650

\[ {}y^{\prime }+3 y = 1 \]

12651

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

12652

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

12653

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

12654

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

12655

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

12656

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

12657

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

12658

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

12659

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

12660

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

12661

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

12662

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

12663

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

12664

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

12665

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

12666

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

12667

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

12668

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

12669

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

12670

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

12671

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

12672

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

12673

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

12674

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

12675

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

12676

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

12677

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

12678

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

12679

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

12680

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

12681

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

12682

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

12683

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

12684

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

12685

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

12686

\[ {}y^{\prime } = 4 y+1 \]

12687

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

12688

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

12689

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

12690

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

12691

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

12692

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

12693

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

12694

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

12695

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

12696

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

12697

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

12698

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

12699

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

12700

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