2.2.167 Problems 16601 to 16700

Table 2.347: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

Maple

Mma

Sympy

time(sec)

16601

\begin{align*} x^{2} y^{\prime \prime }-7 y^{\prime } x +15 y&=x^{2} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

1.238

16602

\begin{align*} x^{2} y^{\prime \prime }-7 y^{\prime } x +15 y&=x \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

1.200

16603

\begin{align*} x^{2} y^{\prime \prime }-7 y^{\prime } x +15 y&=1 \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

1.165

16604

\begin{align*} x^{2} y^{\prime \prime }-7 y^{\prime } x +15 y&=4 x^{2}+2 x +3 \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

1.244

16605

\begin{align*} y^{\prime \prime }+9 y&=52 \,{\mathrm e}^{2 x} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.352

16606

\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=27 \,{\mathrm e}^{6 x} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.386

16607

\begin{align*} y^{\prime \prime }+4 y^{\prime }-5 y&=30 \,{\mathrm e}^{-4 x} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.313

16608

\begin{align*} y^{\prime \prime }+3 y^{\prime }&={\mathrm e}^{\frac {x}{2}} \\ \end{align*}

[[_2nd_order, _missing_y]]

0.843

16609

\begin{align*} y^{\prime \prime }-3 y^{\prime }-10 y&=-5 \,{\mathrm e}^{3 x} \\ y \left (0\right ) &= 5 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.440

16610

\begin{align*} y^{\prime \prime }+9 y&=10 \cos \left (2 x \right )+15 \sin \left (2 x \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.466

16611

\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=25 \sin \left (6 x \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.497

16612

\begin{align*} y^{\prime \prime }+3 y^{\prime }&=26 \cos \left (\frac {x}{3}\right )-12 \sin \left (\frac {x}{3}\right ) \\ \end{align*}

[[_2nd_order, _missing_y]]

1.088

16613

\begin{align*} y^{\prime \prime }+4 y^{\prime }-5 y&=\cos \left (x \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.317

16614

\begin{align*} y^{\prime \prime }-3 y^{\prime }-10 y&=-4 \cos \left (x \right )+7 \sin \left (x \right ) \\ y \left (0\right ) &= 8 \\ y^{\prime }\left (0\right ) &= -5 \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.477

16615

\begin{align*} y^{\prime \prime }-3 y^{\prime }-10 y&=-200 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.261

16616

\begin{align*} y^{\prime \prime }+4 y^{\prime }-5 y&=x^{3} \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.305

16617

\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=18 x^{2}+3 x +4 \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.369

16618

\begin{align*} y^{\prime \prime }+9 y&=9 x^{4}-9 \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.326

16619

\begin{align*} y^{\prime \prime }+9 y&=x^{3} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.441

16620

\begin{align*} y^{\prime \prime }+9 y&=25 x \cos \left (2 x \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.458

16621

\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&={\mathrm e}^{2 x} \sin \left (x \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.422

16622

\begin{align*} y^{\prime \prime }+9 y&=54 x^{2} {\mathrm e}^{3 x} \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.356

16623

\begin{align*} y^{\prime \prime }&=6 \,{\mathrm e}^{x} \sin \left (x \right ) x \\ \end{align*}

[[_2nd_order, _quadrature]]

1.056

16624

\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=\left (-6 x -8\right ) \cos \left (2 x \right )+\left (8 x -11\right ) \sin \left (2 x \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.733

16625

\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=\left (12 x -4\right ) {\mathrm e}^{-5 x} \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.389

16626

\begin{align*} y^{\prime \prime }+9 y&=39 x \,{\mathrm e}^{2 x} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.540

16627

\begin{align*} y^{\prime \prime }-3 y^{\prime }-10 y&=-3 \,{\mathrm e}^{-2 x} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.329

16628

\begin{align*} y^{\prime \prime }+4 y^{\prime }&=20 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.891

16629

\begin{align*} y^{\prime \prime }+4 y^{\prime }&=x^{2} \\ \end{align*}

[[_2nd_order, _missing_y]]

0.874

16630

\begin{align*} y^{\prime \prime }+9 y&=3 \sin \left (3 x \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.388

16631

\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=10 \,{\mathrm e}^{3 x} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.385

16632

\begin{align*} y^{\prime \prime }-3 y^{\prime }-10 y&=\left (72 x^{2}-1\right ) {\mathrm e}^{2 x} \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.360

16633

\begin{align*} y^{\prime \prime }-3 y^{\prime }-10 y&=4 x \,{\mathrm e}^{6 x} \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.336

16634

\begin{align*} y^{\prime \prime }-10 y^{\prime }+25 y&=6 \,{\mathrm e}^{5 x} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.392

16635

\begin{align*} y^{\prime \prime }-10 y^{\prime }+25 y&=6 \,{\mathrm e}^{-5 x} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.413

16636

\begin{align*} 5 y+4 y^{\prime }+y^{\prime \prime }&=24 \sin \left (3 x \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.375

16637

\begin{align*} 5 y+4 y^{\prime }+y^{\prime \prime }&=8 \,{\mathrm e}^{-3 x} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.339

16638

\begin{align*} y^{\prime \prime }-4 y^{\prime }+5 y&={\mathrm e}^{2 x} \sin \left (x \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.363

16639

\begin{align*} y^{\prime \prime }-4 y^{\prime }+5 y&={\mathrm e}^{-x} \sin \left (x \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.349

16640

\begin{align*} y^{\prime \prime }-4 y^{\prime }+5 y&=100 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.283

16641

\begin{align*} y^{\prime \prime }-4 y^{\prime }+5 y&={\mathrm e}^{-x} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.320

16642

\begin{align*} y^{\prime \prime }-4 y^{\prime }+5 y&=10 x^{2}+4 x +8 \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.326

16643

\begin{align*} y^{\prime \prime }+9 y&={\mathrm e}^{2 x} \sin \left (x \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.472

16644

\begin{align*} y^{\prime \prime }+y&=6 \cos \left (x \right )-3 \sin \left (x \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.530

16645

\begin{align*} y^{\prime \prime }+y&=6 \cos \left (2 x \right )-3 \sin \left (2 x \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.457

16646

\begin{align*} y^{\prime \prime }-4 y^{\prime }+5 y&=x^{3} {\mathrm e}^{-x} \sin \left (x \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.663

16647

\begin{align*} y^{\prime \prime }-4 y^{\prime }+5 y&=x^{3} {\mathrm e}^{2 x} \sin \left (x \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.663

16648

\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&=x^{2} {\mathrm e}^{-7 x}+2 \,{\mathrm e}^{-7 x} \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.372

16649

\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&=x^{2} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.301

16650

\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&=4 \,{\mathrm e}^{-8 x} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.310

16651

\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&=4 \,{\mathrm e}^{3 x} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.321

16652

\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&=x^{2} {\mathrm e}^{3 x} \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.345

16653

\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&=\cos \left (2 x \right ) x^{2} \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.689

16654

\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&=x^{2} {\mathrm e}^{3 x} \sin \left (2 x \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.717

16655

\begin{align*} y^{\prime \prime }-4 y^{\prime }+20 y&={\mathrm e}^{4 x} \sin \left (2 x \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.422

16656

\begin{align*} y^{\prime \prime }-4 y^{\prime }+20 y&={\mathrm e}^{2 x} \sin \left (4 x \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.386

16657

\begin{align*} y^{\prime \prime }-4 y^{\prime }+20 y&=x^{3} \sin \left (4 x \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.697

16658

\begin{align*} y^{\prime \prime }-10 y^{\prime }+25 y&=3 x^{2} {\mathrm e}^{5 x} \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.404

16659

\begin{align*} y^{\prime \prime }-10 y^{\prime }+25 y&=3 x^{4} \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.411

16660

\begin{align*} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }&=12 \,{\mathrm e}^{-2 x} \\ \end{align*}

[[_high_order, _missing_y]]

0.105

16661

\begin{align*} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }&=10 \sin \left (2 x \right ) \\ \end{align*}

[[_high_order, _missing_y]]

0.124

16662

\begin{align*} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }&=32 \,{\mathrm e}^{4 x} \\ \end{align*}

[[_high_order, _missing_y]]

0.112

16663

\begin{align*} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }&=32 x \\ \end{align*}

[[_high_order, _missing_y]]

0.110

16664

\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=x^{2} \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.107

16665

\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=30 \cos \left (2 x \right ) \\ \end{align*}

[[_3rd_order, _linear, _nonhomogeneous]]

0.125

16666

\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=6 \,{\mathrm e}^{x} \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.115

16667

\begin{align*} y^{\left (5\right )}+18 y^{\prime \prime \prime }+81 y^{\prime }&=x^{2} {\mathrm e}^{3 x} \\ \end{align*}

[[_high_order, _missing_y]]

0.148

16668

\begin{align*} y^{\left (5\right )}+18 y^{\prime \prime \prime }+81 y^{\prime }&=x^{2} \sin \left (3 x \right ) \\ \end{align*}

[[_high_order, _missing_y]]

0.749

16669

\begin{align*} y^{\left (5\right )}+18 y^{\prime \prime \prime }+81 y^{\prime }&=x^{2} {\mathrm e}^{3 x} \sin \left (3 x \right ) \\ \end{align*}

[[_high_order, _missing_y]]

0.385

16670

\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=30 x \cos \left (2 x \right ) \\ \end{align*}

[[_3rd_order, _linear, _nonhomogeneous]]

0.191

16671

\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=3 \cos \left (x \right ) x \\ \end{align*}

[[_3rd_order, _linear, _nonhomogeneous]]

0.535

16672

\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=3 \,{\mathrm e}^{x} \cos \left (x \right ) x \\ \end{align*}

[[_3rd_order, _linear, _nonhomogeneous]]

0.168

16673

\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=5 x^{5} {\mathrm e}^{2 x} \\ \end{align*}

[[_3rd_order, _linear, _nonhomogeneous]]

0.148

16674

\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=27 \,{\mathrm e}^{6 x}+25 \sin \left (6 x \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.660

16675

\begin{align*} y^{\prime \prime }+9 y&=25 x \cos \left (2 x \right )+3 \sin \left (3 x \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.845

16676

\begin{align*} y^{\prime \prime }-4 y^{\prime }+5 y&=5 \sin \left (x \right )^{2} \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.397

16677

\begin{align*} y^{\prime \prime }-4 y^{\prime }+5 y&=20 \sinh \left (x \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.550

16678

\begin{align*} x^{2} y^{\prime \prime }-5 y^{\prime } x +8 y&=\frac {5}{x^{3}} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

1.477

16679

\begin{align*} 2 x^{2} y^{\prime \prime }-y^{\prime } x +y&=\frac {50}{x^{3}} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

1.638

16680

\begin{align*} 2 x^{2} y^{\prime \prime }+5 y^{\prime } x +y&=85 \cos \left (2 \ln \left (x \right )\right ) \\ \end{align*}

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

3.092

16681

\begin{align*} x^{2} y^{\prime \prime }-2 y&=15 \cos \left (3 \ln \left (x \right )\right )-10 \sin \left (3 \ln \left (x \right )\right ) \\ \end{align*}

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

1.189

16682

\begin{align*} 3 x^{2} y^{\prime \prime }-7 y^{\prime } x +3 y&=4 x^{3} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

1.530

16683

\begin{align*} 2 x^{2} y^{\prime \prime }+5 y^{\prime } x +y&=\frac {10}{x} \\ \end{align*}

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

1.797

16684

\begin{align*} x^{2} y^{\prime \prime }-5 y^{\prime } x +9 y&=6 x^{3} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

1.447

16685

\begin{align*} x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y&=64 \ln \left (x \right ) x^{2} \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

1.420

16686

\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=3 \sqrt {x} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

1.717

16687

\begin{align*} y^{\prime \prime }+y&=\cot \left (x \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.450

16688

\begin{align*} 4 y+y^{\prime \prime }&=\csc \left (2 x \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.605

16689

\begin{align*} y^{\prime \prime }-7 y^{\prime }+10 y&=6 \,{\mathrm e}^{3 x} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.328

16690

\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=\left (24 x^{2}+2\right ) {\mathrm e}^{2 x} \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.440

16691

\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=\frac {{\mathrm e}^{-2 x}}{x^{2}+1} \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.491

16692

\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -y&=\sqrt {x} \\ \end{align*}

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

2.058

16693

\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -9 y&=12 x^{3} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

1.684

16694

\begin{align*} x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=x^{2} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

1.384

16695

\begin{align*} x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y&=\ln \left (x \right ) \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

1.349

16696

\begin{align*} x^{2} y^{\prime \prime }-2 y&=\frac {1}{x -2} \\ \end{align*}

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

0.700

16697

\begin{align*} y^{\prime \prime } x -y^{\prime }-4 x^{3} y&=x^{3} {\mathrm e}^{x^{2}} \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

1.601

16698

\begin{align*} y^{\prime \prime } x +\left (2 x +2\right ) y^{\prime }+2 y&=8 \,{\mathrm e}^{2 x} \\ \end{align*}

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

1.184

16699

\begin{align*} \left (x +1\right ) y^{\prime \prime }+y^{\prime } x -y&=\left (x +1\right )^{2} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.913

16700

\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x -4 y&=\frac {10}{x} \\ y \left (1\right ) &= 3 \\ y^{\prime }\left (1\right ) &= -15 \\ \end{align*}

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

1.543