6.58 Problems 5701 to 5800

Table 6.115: Main lookup table sequentially arranged

#

ODE

Mathematica

Maple

Sympy

5701

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

5702

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

5703

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

5704

\[ {} {\mathrm e}^{y^{\prime }-y}-{y^{\prime }}^{2}+1 = 0 \]

5705

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

5706

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

5707

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

5708

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

5709

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

5710

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

5711

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

5712

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

5713

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

5714

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

5715

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

5716

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

5717

\[ {} y^{\prime \prime } = \operatorname {c1} \cos \left (a x \right )+\operatorname {c2} \sin \left (b x \right ) \]

5718

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

5719

\[ {} y^{\prime \prime } = \operatorname {c1} \,{\mathrm e}^{a x}+\operatorname {c2} \,{\mathrm e}^{-b x} \]

5720

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

5721

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

5722

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

5723

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

5724

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

5725

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

5726

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

5727

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

5728

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

5729

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

5730

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

5731

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

5732

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

5733

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

5734

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

5735

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

5736

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

5737

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

5738

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

5739

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

5740

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

5741

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

5742

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

5743

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

5744

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

5745

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

5746

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

5747

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

5748

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

5749

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

5750

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

5751

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

5752

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

5753

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

5754

\[ {} \left (x^{4}+\operatorname {a1} \,x^{2}+\operatorname {a0} \right ) y+y^{\prime \prime } = 0 \]

5755

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

5756

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

5757

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

5758

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

5759

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

5760

\[ {} \left (\operatorname {a0} +\operatorname {a1} \cos \left (x \right )^{2}+\operatorname {a2} \csc \left (x \right )^{2}\right ) y+y^{\prime \prime } = 0 \]

5761

\[ {} y^{\prime \prime } = \left (a^{2}+\left (-1+p \right ) p \csc \left (x \right )^{2}+\left (-1+q \right ) q \sec \left (x \right )^{2}\right ) y \]

5762

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

5763

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

5764

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

5765

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

5766

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

5767

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

5768

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

5769

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

5770

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

5771

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

5772

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

5773

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

5774

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

5775

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

5776

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

5777

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

5778

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

5779

\[ {} y-2 y^{\prime }+y^{\prime \prime } = 8 x^{2} {\mathrm e}^{3 x} \]

5780

\[ {} y-2 y^{\prime }+y^{\prime \prime } = 50 \cosh \left (x \right ) \cos \left (x \right ) \]

5781

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

5782

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

5783

\[ {} 5 y+2 y^{\prime }+y^{\prime \prime } = 0 \]

5784

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

5785

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

5786

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

5787

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

5788

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

5789

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

5790

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

5791

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

5792

\[ {} -4 y-3 y^{\prime }+y^{\prime \prime } = 0 \]

5793

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

5794

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

5795

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

5796

\[ {} 5 y+4 y^{\prime }+y^{\prime \prime } = 0 \]

5797

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

5798

\[ {} y^{\prime \prime }-4 y^{\prime }+13 y = 0 \]

5799

\[ {} 6 y-5 y^{\prime }+y^{\prime \prime } = 0 \]

5800

\[ {} 6 y-5 y^{\prime }+y^{\prime \prime } = 4 x^{2} {\mathrm e}^{x} \]