4.7.6 Problems 501 to 600

Table 4.759: Solved using series method

#

ODE

Mathematica

Maple

Sympy

2449

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

2450

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

2451

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

2452

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

2453

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

2454

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

2455

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

2456

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

2457

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

2458

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

2459

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

2460

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

2461

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

2462

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

2463

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

2464

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

2465

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

2466

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

2467

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

2468

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

2469

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

2470

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

2471

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

2611

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

2612

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

2613

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

2614

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

2615

\[ {} t \left (2-t \right ) y^{\prime \prime }-6 \left (t -1\right ) y^{\prime }-4 y = 0 \]

2616

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

2617

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

2618

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

2619

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

2620

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

2621

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

2622

\[ {} y^{\prime \prime }+t^{3} y^{\prime }+3 t^{2} y = {\mathrm e}^{t} \]

2623

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

2624

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

2625

\[ {} y^{\prime \prime }+t y^{\prime }+{\mathrm e}^{t} y = 0 \]

2626

\[ {} y^{\prime \prime }+y^{\prime }+{\mathrm e}^{t} y = 0 \]

2627

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

2638

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

2639

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

2640

\[ {} \sin \left (t \right ) y^{\prime \prime }+\cos \left (t \right ) y^{\prime }+\frac {y}{t} = 0 \]

2641

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

2642

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

2643

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

2644

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

2645

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

2646

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

2647

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

2648

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

2649

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

2650

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

2651

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

2652

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

2653

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

2654

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

2655

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

2656

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

2657

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

2658

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

2659

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

2660

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

2661

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

2662

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

2663

\[ {} t \left (1-t \right ) y^{\prime \prime }+\left (\gamma -\left (\alpha +\beta +1\right ) t \right ) y^{\prime }-\alpha \beta y = 0 \]

2664

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

2665

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

2666

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

2667

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

2668

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

2669

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

2670

\[ {} t^{2} y^{\prime \prime }+t p \left (t \right ) y^{\prime }+q \left (t \right ) y = 0 \]

3335

\[ {} y^{\prime } = \sqrt {1-y} \]

3336

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

3337

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

3338

\[ {} y^{\prime } = 3 x +\frac {y}{x} \]

3339

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

3340

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

3341

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

3342

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

3343

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

3344

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

3345

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

3346

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

3347

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

3348

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

3349

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

3350

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

3351

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

3352

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

3353

\[ {} x^{2} \left (x +4\right ) y^{\prime \prime }+7 x y^{\prime }-y = 0 \]

3354

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

3355

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

3356

\[ {} 9 x^{2} y^{\prime \prime }+\left (2+3 x \right ) y = 0 \]

3357

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

3358

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

3359

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

3360

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

3361

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