4.4.27 Problems 2601 to 2700

Table 4.597: Second ODE homogeneous ODE

#

ODE

Mathematica

Maple

Sympy

12367

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

12368

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

12369

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

12370

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

12371

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

12373

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

12374

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

12375

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

12376

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

12377

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

12378

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

12379

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

12380

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

12382

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

12383

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

12384

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

12385

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

12386

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

12387

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

12388

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

12389

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

12391

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

12392

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

12393

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

12394

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

12395

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

12396

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

12397

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

12398

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

12399

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

12400

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

12401

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

12402

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

12403

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

12404

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

12405

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

12407

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

12408

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

12409

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

12410

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

12411

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

12412

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

12413

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

12414

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

12415

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

12416

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

12417

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

12418

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

12419

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

12420

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

12421

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

12422

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

12423

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

12424

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

12425

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

12426

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

12427

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

12428

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

12429

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

12430

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

12431

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

12432

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

12433

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

12434

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

12435

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

12436

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

12438

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

12439

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

12441

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

12442

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

12443

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

12445

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

12446

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

12448

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

12449

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

12450

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

12451

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

12452

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

12453

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

12454

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

12457

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

12460

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

12462

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

12466

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

12468

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

12469

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

12470

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

12471

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

12472

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

12473

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

12474

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

12475

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

12476

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

12477

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

12478

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

12479

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

12480

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

12481

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

12482

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

12483

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