3.4.18 Problems 1701 to 1800

Table 3.371: Second ODE homogeneous ODE

#

ODE

Mathematica

Maple

9454

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

9456

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

9457

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

9458

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

9459

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

9460

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

9461

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

9462

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

9463

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

9464

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

9465

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

9466

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

9467

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

9468

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

9469

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

9470

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

9471

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

9472

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

9473

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

9474

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

9475

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

9476

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

9477

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

9478

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

9479

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

9480

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

9481

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

9482

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

9483

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

9484

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

9485

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

9487

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

9488

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

9490

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

9491

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

9492

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

9494

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

9495

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

9497

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

9498

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

9499

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

9500

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

9501

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

9502

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

9503

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

9506

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

9509

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

9511

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

9515

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

9517

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

9518

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

9519

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

9520

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

9521

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

9522

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

9523

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

9524

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

9525

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

9526

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

9527

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

9528

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

9529

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

9530

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

9531

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

9532

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

9533

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

9534

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

9535

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

9536

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

9537

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

9538

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

9539

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

9540

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

9541

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

9542

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

9543

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

9544

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

9545

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

9546

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

9547

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

9548

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

9549

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

9550

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

9551

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

9552

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

9553

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

9554

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

9555

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

9556

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

9557

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

9558

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

9560

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

9561

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

9564

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

9565

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

9566

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

9568

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

9569

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

9570

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

9571

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