3.4.17 Problems 1601 to 1700

Table 3.369: Second ODE homogeneous ODE

#

ODE

Mathematica

Maple

9340

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

9343

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

9344

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

9345

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

9346

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

9347

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

9348

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

9349

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

9350

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

9351

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

9352

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

9353

\[ {}y^{\prime \prime }-\left (4 a^{2} b^{2} x^{2} {\mathrm e}^{2 b \,x^{2}}-1\right ) y = 0 \]

9354

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

9355

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

9356

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

9357

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

9358

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

9359

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

9360

\[ {}y^{\prime \prime }-\left (n \left (n +1\right ) \operatorname {WeierstrassP}\left (x , \operatorname {g2} , \operatorname {g3}\right )+B \right ) y = 0 \]

9361

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

9363

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

9364

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

9365

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

9366

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

9367

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

9368

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

9370

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

9371

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

9372

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

9373

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

9374

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

9375

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

9376

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

9377

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

9378

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

9379

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

9380

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

9381

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

9383

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

9385

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

9386

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

9387

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

9388

\[ {}y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+\left (\operatorname {a1} \,x^{2}+\operatorname {b1} x +\operatorname {c1} \right ) y = 0 \]

9389

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

9390

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

9391

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

9392

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

9393

\[ {}y^{\prime \prime }+a \,x^{q -1} y^{\prime }+b \,x^{q -2} y = 0 \]

9395

\[ {}y^{\prime \prime }-\frac {y^{\prime }}{\sqrt {x}}+\frac {\left (x +\sqrt {x}-8\right ) y}{4 x^{2}} = 0 \]

9398

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

9399

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

9400

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

9401

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

9402

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

9403

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

9404

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

9405

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

9406

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

9407

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

9409

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

9410

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

9411

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

9412

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

9414

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

9415

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

9416

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

9417

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

9418

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

9419

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

9420

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

9422

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

9423

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

9424

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

9425

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

9426

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

9427

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

9428

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

9429

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

9431

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

9432

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

9433

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

9434

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

9435

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

9436

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

9437

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

9438

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

9440

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

9441

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

9442

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

9443

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

9444

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

9445

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

9446

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

9447

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

9448

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

9449

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

9450

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

9451

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

9452

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

9453

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