6.48 Problems 4701 to 4800

Table 6.95: Main lookup table sequentially arranged

#

ODE

Mathematica

Maple

Sympy

4701

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

4702

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

4703

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

4704

\[ {} y^{\prime } = a \,x^{\frac {n}{-n +1}}+b y^{n} \]

4705

\[ {} y^{\prime } = f \left (x \right ) y+g \left (x \right ) y^{k} \]

4706

\[ {} y^{\prime } = f \left (x \right )+g \left (x \right ) y+h \left (x \right ) y^{n} \]

4707

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

4708

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

4709

\[ {} y^{\prime } = a +b y-\sqrt {A +B y} \]

4710

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

4711

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

4712

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

4713

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

4714

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

4715

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

4716

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

4717

\[ {} y^{\prime } = a +b \cos \left (A x +B y\right ) \]

4718

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

4719

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

4720

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

4721

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

4722

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

4723

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

4724

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

4725

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

4726

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

4727

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

4728

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

4729

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

4730

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

4731

\[ {} y^{\prime } = a +b \sin \left (A x +B y\right ) \]

4732

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

4733

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

4734

\[ {} y^{\prime } = \sqrt {a +\cos \left (y\right ) b} \]

4735

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

4736

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

4737

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

4738

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

4739

\[ {} y^{\prime } = x^{m -1} y^{-n +1} f \left (a \,x^{m}+b y^{n}\right ) \]

4740

\[ {} y^{\prime } = a f \left (y\right ) \]

4741

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

4742

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

4743

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

4744

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

4745

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

4746

\[ {} 2 y^{\prime }+a x = \sqrt {a^{2} x^{2}-4 b \,x^{2}-4 c y} \]

4747

\[ {} 2 y^{\prime }+a x = -\sqrt {a^{2} x^{2}-4 b \,x^{2}-4 c y} \]

4748

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

4749

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

4750

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

4751

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

4752

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

4753

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

4754

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

4755

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

4756

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

4757

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

4758

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

4759

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

4760

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

4761

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

4762

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

4763

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

4764

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

4765

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

4766

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

4767

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

4768

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

4769

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

4770

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

4771

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

4772

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

4773

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

4774

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

4775

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

4776

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

4777

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

4778

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

4779

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

4780

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

4781

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

4782

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

4783

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

4784

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

4785

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

4786

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

4787

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

4788

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

4789

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

4790

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

4791

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

4792

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

4793

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

4794

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

4795

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

4796

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

4797

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

4798

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

4799

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

4800

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