4.9.54 Problems 5301 to 5400

Table 4.945: First order ode linear in derivative

#

ODE

Mathematica

Maple

Sympy

14594

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

14595

\[ {} y^{\prime }+\frac {3 y}{x} = 6 x^{2} \]

14596

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

14597

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

14598

\[ {} y^{\prime }+4 x y = 8 x \]

14599

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

14600

\[ {} \left (u^{2}+1\right ) v^{\prime }+4 u v = 3 u \]

14601

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

14602

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

14603

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

14604

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

14605

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

14606

\[ {} \cos \left (t \right ) r^{\prime }+r \sin \left (t \right )-\cos \left (t \right )^{4} = 0 \]

14607

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

14608

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

14609

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

14610

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

14611

\[ {} y^{\prime }+\left (4 y-\frac {8}{y^{3}}\right ) x = 0 \]

14612

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

14613

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

14614

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

14615

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

14616

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

14617

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

14618

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

14619

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

14620

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

14621

\[ {} y^{\prime }+y = \left \{\begin {array}{cc} 2 & 0\le x <1 \\ 0 & 1\le x \end {array}\right . \]

14622

\[ {} y^{\prime }+y = \left \{\begin {array}{cc} 5 & 0\le x <10 \\ 1 & 10\le x \end {array}\right . \]

14623

\[ {} y^{\prime }+y = \left \{\begin {array}{cc} {\mathrm e}^{-x} & 0\le x <2 \\ {\mathrm e}^{-2} & 2\le x \end {array}\right . \]

14624

\[ {} \left (x +2\right ) y^{\prime }+y = \left \{\begin {array}{cc} 2 x & 0\le x <2 \\ 4 & 2\le x \end {array}\right . \]

14625

\[ {} a y^{\prime }+b y = k \,{\mathrm e}^{-\lambda x} \]

14626

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

14627

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

14628

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

14629

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

14630

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

14631

\[ {} y^{\prime } = -8 x y^{2}+4 x \left (1+4 x \right ) y-8 x^{3}-4 x^{2}+1 \]

14632

\[ {} 6 x^{2} y-\left (x^{3}+1\right ) y^{\prime } = 0 \]

14633

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

14634

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

14635

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

14636

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

14637

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

14638

\[ {} 8 x^{3} y-12 x^{3}+\left (x^{4}+1\right ) y^{\prime } = 0 \]

14639

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

14640

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

14641

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

14642

\[ {} y^{\prime } = \frac {2 x -7 y}{3 y-8 x} \]

14643

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

14644

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

14645

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

14646

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

14647

\[ {} 8+2 y^{2}+\left (-x^{2}+1\right ) y y^{\prime } = 0 \]

14648

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

14649

\[ {} 3 x^{2}+2 x y^{2}+\left (2 x^{2} y+6 y^{2}\right ) y^{\prime } = 0 \]

14650

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

14651

\[ {} y^{\prime } = \frac {2 x +7 y}{2 x -2 y} \]

14652

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

14653

\[ {} y^{\prime }+y = \left \{\begin {array}{cc} 1 & 0\le x <2 \\ 0 & 0<x \end {array}\right . \]

14654

\[ {} \left (x +2\right ) y^{\prime }+y = \left \{\begin {array}{cc} 2 x & 0\le x \le 2 \\ 4 & 2<x \end {array}\right . \]

14655

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

14656

\[ {} 5 x y+4 y^{2}+1+\left (x^{2}+2 x y\right ) y^{\prime } = 0 \]

14657

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

14658

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

14659

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

14660

\[ {} 4 x y^{2}+6 y+\left (5 x^{2} y+8 x \right ) y^{\prime } = 0 \]

14661

\[ {} 8 x^{2} y^{3}-2 y^{4}+\left (5 y^{2} x^{3}-8 x y^{3}\right ) y^{\prime } = 0 \]

14662

\[ {} 5 x +2 y+1+\left (2 x +y+1\right ) y^{\prime } = 0 \]

14663

\[ {} 3 x -y+1-\left (6 x -2 y-3\right ) y^{\prime } = 0 \]

14664

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

14665

\[ {} 10 x -4 y+12-\left (x +5 y+3\right ) y^{\prime } = 0 \]

14666

\[ {} 6 x +4 y+1+\left (4 x +2 y+2\right ) y^{\prime } = 0 \]

14667

\[ {} 3 x -y-6+\left (x +y+2\right ) y^{\prime } = 0 \]

14668

\[ {} 2 x +3 y+1+\left (4 x +6 y+1\right ) y^{\prime } = 0 \]

14669

\[ {} \left (x +y+1\right ) y^{\prime }+1+4 x +3 y = 0 \]

14925

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

14926

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

14985

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

14986

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

14987

\[ {} u^{\prime } = 4 t \ln \left (t \right ) \]

14988

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

14989

\[ {} T^{\prime } = {\mathrm e}^{-t} \sin \left (2 t \right ) \]

14990

\[ {} x^{\prime } = \sec \left (t \right )^{2} \]

14991

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

14992

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

14993

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

14994

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

14995

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

14996

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

14997

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

14998

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

14999

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

15000

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

15001

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

15002

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

15003

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

15004

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

15005

\[ {} x^{\prime }+p x = q \]

15006

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