2.95 Problems 9401 to 9500

Table 2.189: Main lookup table

#

ODE

Mathematica result

Maple result

9401

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

9402

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

9403

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

9404

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

9405

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

9406

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

9407

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

9408

\[ {}y^{\prime \prime }+\frac {\left (11 \operatorname {WeierstrassP}\left (x , a , b\right ) \operatorname {WeierstrassPPrime}\left (x , a , b\right )-6 \operatorname {WeierstrassP}\left (x , a , b\right )^{2}+\frac {a}{2}\right ) y^{\prime }}{\operatorname {WeierstrassPPrime}\left (x , a , b\right )+\operatorname {WeierstrassP}\left (x , a , b\right )^{2}}+\frac {\left (\operatorname {WeierstrassPPrime}\left (x , a , b\right )^{2}-\operatorname {WeierstrassP}\left (x , a , b\right )^{2} \operatorname {WeierstrassPPrime}\left (x , a , b\right )-\operatorname {WeierstrassP}\left (x , a , b\right ) \left (6 \operatorname {WeierstrassP}\left (x , a , b\right )^{2}-\frac {a}{2}\right )\right ) y}{\operatorname {WeierstrassPPrime}\left (x , a , b\right )+\operatorname {WeierstrassP}\left (x , a , b\right )^{2}} = 0 \]

9409

\[ {}y^{\prime \prime }+\frac {k^{2} \operatorname {JacobiSN}\left (x , k\right ) \operatorname {JacobiCN}\left (x , k\right ) y^{\prime }}{\operatorname {JacobiDN}\left (x , k\right )}+n^{2} y \operatorname {JacobiDN}\left (x , k\right )^{2} = 0 \]

9410

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

9411

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

9412

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

9413

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

9414

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

9415

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

9416

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

9417

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

9418

\[ {}y^{\prime \prime }-\frac {f^{\prime }\left (x \right ) y^{\prime }}{f \left (x \right )}+\left (\frac {3 {f^{\prime }\left (x \right )}^{2}}{4 f \left (x \right )^{2}}-\frac {f^{\prime \prime }\left (x \right )}{2 f \left (x \right )}-\frac {3 {g^{\prime \prime }\left (x \right )}^{2}}{4 {g^{\prime }\left (x \right )}^{2}}+\frac {g^{\prime \prime \prime }\left (x \right )}{2 g^{\prime }\left (x \right )}+\frac {\left (\frac {1}{4}-v^{2}\right ) {g^{\prime }\left (x \right )}^{2}}{g \left (x \right )^{2}}+{g^{\prime }\left (x \right )}^{2}\right ) y = 0 \]

9419

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

9420

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

9421

\[ {}4 y^{\prime \prime }+9 x y = 0 \]

9422

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

9423

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

9424

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

9425

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

9426

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

9427

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

9428

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

9429

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

9430

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

9431

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

9432

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

9433

\[ {}x y^{\prime \prime }-y^{\prime }-y a \,x^{3} = 0 \]

9434

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

9435

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

9436

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

9437

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

9438

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

9439

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

9440

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

9441

\[ {}x y^{\prime \prime }+a y^{\prime }+b \,x^{\operatorname {a1}} y = 0 \]

9442

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

9443

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

9444

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

9445

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

9446

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

9447

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

9448

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

9449

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

9450

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

9451

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

9452

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

9453

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

9454

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

9455

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

9456

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

9457

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

9458

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

9459

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

9460

\[ {}x y^{\prime \prime }+\left (4 x^{2}-1\right ) y^{\prime }-4 x^{3} y-4 x^{5} = 0 \]

9461

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

9462

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

9463

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

9464

\[ {}\left (-3+x \right ) y^{\prime \prime }-\left (4 x -9\right ) y^{\prime }+\left (3 x -6\right ) y = 0 \]

9465

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

9466

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

9467

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

9468

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

9469

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

9470

\[ {}4 x y^{\prime \prime }+2 y^{\prime }-y = 0 \]

9471

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

9472

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

9473

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

9474

\[ {}16 x y^{\prime \prime }+8 y^{\prime }-\left (x +a \right ) y = 0 \]

9475

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

9476

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

9477

\[ {}5 \left (a x +b \right ) y^{\prime \prime }+8 a y^{\prime }+c \left (a x +b \right )^{\frac {1}{5}} y = 0 \]

9478

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

9479

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

9480

\[ {}\left (\operatorname {a2} x +\operatorname {b2} \right ) y^{\prime \prime }+\left (\operatorname {a1} x +\operatorname {b1} \right ) y^{\prime }+\left (\operatorname {a0} x +\operatorname {b0} \right ) y = 0 \]

9481

\[ {}x^{2} y^{\prime \prime }-6 y = 0 \]

9482

\[ {}x^{2} y^{\prime \prime }-12 y = 0 \]

9483

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

9484

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

9485

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

9486

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

9487

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

9488

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

9489

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

9490

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

9491

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

9492

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

9493

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

9494

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

9495

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

9496

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

9497

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

9498

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

9499

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

9500

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