2.48 Problems 4701 to 4800

Table 2.48: Main lookup table

#

ODE

Mathematica result

Maple result

4701

\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 3 \,{\mathrm e}^{-2 x} \]

4702

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

4703

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

4704

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

4705

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

4706

\[ {}x^{\prime \prime }+4 x^{\prime }+4 x = 0 \]

4707

\[ {}q^{\prime \prime }+9 q^{\prime }+14 q = \frac {\sin \relax (t )}{2} \]

4708

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

4709

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

4710

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

4711

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

4712

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

4713

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

4714

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

4715

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

4716

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

4717

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

4718

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

4719

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

4720

\[ {}x^{3} \left (x +1\right ) y^{\prime \prime \prime }-\left (2+4 x \right ) x^{2} y^{\prime \prime }+\left (4+10 x \right ) x y^{\prime }-\left (4+12 x \right ) y = 0 \]

4721

\[ {}x^{3} \left (x^{2}+1\right ) y^{\prime \prime \prime }-\left (4 x^{2}+2\right ) x^{2} y^{\prime \prime }+\left (10 x^{2}+4\right ) x y^{\prime }-\left (12 x^{2}+4\right ) y = 0 \]

4722

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

4723

\[ {}\left (1-x \right ) x^{2} y^{\prime \prime }+\left (5 x -4\right ) x y^{\prime }+\left (6-9 x \right ) y = 0 \]

4724

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

4725

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

4726

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

4727

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

4728

\[ {}y^{\prime \prime }-2 x y^{\prime }+8 y = 0 \]

4729

\[ {}y^{\prime \prime }-2 x y^{\prime }+8 y = 0 \]

4730

\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+12 y = 0 \]

4731

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

4732

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

4733

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

4734

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

4735

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

4736

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

4737

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

4738

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

4739

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

4740

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

4741

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

4742

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}+\frac {9}{4}\right ) y = 0 \]

4743

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}+\frac {25}{4}\right ) y = 0 \]

4744

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

4745

\[ {}y^{\prime }+x y = \cos \relax (x ) \]

4746

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

4747

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

4748

\[ {}x y^{\prime \prime }-2 y^{\prime }+y = \cos \relax (x ) \]

4749

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

4750

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

4751

\[ {}y^{\prime \prime }+4 x y = 0 \]

4752

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

4753

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

4754

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

4755

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

4756

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

4757

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

4758

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

4759

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

4760

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

4761

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

4762

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

4763

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

4764

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

4765

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

4766

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

4767

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

4768

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

4769

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

4770

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

4771

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

4772

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

4773

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

4774

\[ {}x y^{\prime \prime }+x^{5} y^{\prime }+y = 0 \]

4775

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

4776

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

4777

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

4778

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

4779

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

4780

\[ {}\left (x^{2}-25\right ) y^{\prime \prime }+2 x y^{\prime }+y = 0 \]

4781

\[ {}\left (x^{2}-25\right ) y^{\prime \prime }+2 x y^{\prime }+y = 0 \]

4782

\[ {}\left (x^{2}-2 x +10\right ) y^{\prime \prime }+x y^{\prime }-4 y = 0 \]

4783

\[ {}\left (x^{2}-2 x +10\right ) y^{\prime \prime }+x y^{\prime }-4 y = 0 \]

4784

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

4785

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

4786

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

4787

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

4788

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

4789

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

4790

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

4791

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

4792

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

4793

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

4794

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

4795

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

4796

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

4797

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

4798

\[ {}y^{\prime \prime }-2 x y^{\prime }+8 y = 0 \]

4799

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

4800

\[ {}y^{\prime \prime }+y \sin \relax (x ) = 0 \]