4.8.10 Problems 901 to 1000

Table 4.813: Third and higher order ode

#

ODE

Mathematica

Maple

Sympy

12823

\[ {} x^{4} y^{\prime \prime \prime \prime }+4 x^{3} y^{\prime \prime \prime }-\left (4 n^{2}+3\right ) x^{2} y^{\prime \prime }+\left (12 n^{2}-3\right ) x y^{\prime }-\left (4 x^{4}+12 n^{2}-3\right ) y = 0 \]

12824

\[ {} x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+\left (4 x^{4}+\left (-\rho ^{2}-\sigma ^{2}+7\right ) x^{2}\right ) y^{\prime \prime }+\left (16 x^{3}+\left (-\rho ^{2}-\sigma ^{2}+1\right ) x \right ) y^{\prime }+\left (\rho ^{2} \sigma ^{2}+8 x^{2}\right ) y = 0 \]

12825

\[ {} x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+\left (4 x^{4}+\left (-2 \mu ^{2}-2 \nu ^{2}+7\right ) x^{2}\right ) y^{\prime \prime }+\left (16 x^{3}+\left (-2 \mu ^{2}-2 \nu ^{2}+1\right ) x \right ) y^{\prime }+\left (8 x^{2}+\left (\mu ^{2}-\nu ^{2}\right )^{2}\right ) y = 0 \]

12826

\[ {} 12 x^{2} y^{\prime \prime }+8 x^{3} y^{\prime \prime \prime }+x^{4} y^{\prime \prime \prime \prime } = 0 \]

12827

\[ {} a y+12 x^{2} y^{\prime \prime }+8 x^{3} y^{\prime \prime \prime }+x^{4} y^{\prime \prime \prime \prime } = 0 \]

12828

\[ {} x^{4} y^{\prime \prime \prime \prime }+\left (6-4 a \right ) x^{3} y^{\prime \prime \prime }+\left (4 b^{2} c^{2} x^{2 c}+6 \left (a -1\right )^{2}-2 c^{2} \left (\mu ^{2}+\nu ^{2}\right )+1\right ) x^{2} y^{\prime \prime }+\left (4 \left (3 c -2 a +1\right ) b^{2} c^{2} x^{2 c}+\left (2 a -1\right ) \left (2 c^{2} \left (\mu ^{2}+\nu ^{2}\right )-2 \left (a -1\right ) a -1\right )\right ) x y^{\prime }+\left (4 \left (a -c \right ) \left (a -2 c \right ) b^{2} c^{2} x^{2 c}+\left (c \mu +c \nu +a \right ) \left (c \mu +c \nu -a \right ) \left (c \mu -c \nu +a \right ) \left (c \mu -c \nu -a \right )\right ) y = 0 \]

12829

\[ {} x^{4} y^{\prime \prime \prime \prime }+\left (6-4 a -4 c \right ) x^{3} y^{\prime \prime \prime }+\left (-2 \nu ^{2} c^{2}+2 a^{2}+4 \left (a +c -1\right )^{2}+4 \left (a -1\right ) \left (c -1\right )-1\right ) x^{2} y^{\prime \prime }+\left (2 \nu ^{2} c^{2}-2 a^{2}-\left (2 a -1\right ) \left (2 c -1\right )\right ) \left (2 a +2 c -1\right ) x y^{\prime }+\left (\left (-\nu ^{2} c^{2}+a^{2}\right ) \left (-\nu ^{2} c^{2}+a^{2}+4 a c +4 c^{2}\right )-b^{4} c^{4} x^{4 c}\right ) y = 0 \]

12830

\[ {} \nu ^{4} x^{4} y^{\prime \prime \prime \prime }+\left (4 \nu -2\right ) \nu ^{3} x^{3} y^{\prime \prime \prime }+\left (\nu -1\right ) \left (2 \nu -1\right ) \nu ^{2} x^{2} y^{\prime \prime }-\frac {b^{4} x^{\frac {2}{\nu }} y}{16} = 0 \]

12831

\[ {} \left (x^{2}-1\right )^{2} y^{\prime \prime \prime \prime }+10 x \left (x^{2}-1\right ) y^{\prime \prime \prime }+\left (24 x^{2}-8-2 \left (\mu \left (\mu +1\right )+\nu \left (\nu +1\right )\right ) \left (x^{2}-1\right )\right ) y^{\prime \prime }-6 x \left (\mu \left (\mu +1\right )+\nu \left (\nu +1\right )-2\right ) y^{\prime }+\left (\left (\mu \left (\mu +1\right )-\nu \left (\nu +1\right )\right )^{2}-2 \mu \left (\mu +1\right )-2 \nu \left (\nu +1\right )\right ) y = 0 \]

12832

\[ {} \left ({\mathrm e}^{x}+2 x \right ) y^{\prime \prime \prime \prime }+4 \left ({\mathrm e}^{x}+2\right ) y^{\prime \prime \prime }+6 \,{\mathrm e}^{x} y^{\prime \prime }+4 \,{\mathrm e}^{x} y^{\prime }+y \,{\mathrm e}^{x}-\frac {1}{x^{5}} = 0 \]

12833

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

12834

\[ {} y^{\prime \prime \prime \prime } \sin \left (x \right )^{6}+4 y^{\prime \prime \prime } \sin \left (x \right )^{5} \cos \left (x \right )-6 y^{\prime \prime } \sin \left (x \right )^{6}-4 y^{\prime } \sin \left (x \right )^{5} \cos \left (x \right )+y \sin \left (x \right )^{6}-f = 0 \]

12835

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

12836

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

12837

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

12838

\[ {} y^{\left (5\right )}+2 y^{\prime \prime \prime }+y^{\prime }-a x -b \sin \left (x \right )-c \cos \left (x \right ) = 0 \]

12839

\[ {} y^{\left (6\right )}+y-\sin \left (\frac {3 x}{2}\right ) \sin \left (\frac {x}{2}\right ) = 0 \]

12840

\[ {} y^{\left (5\right )}-a x y-b = 0 \]

12841

\[ {} y^{\left (5\right )}+a \,x^{\nu } y^{\prime }+a \nu \,x^{\nu -1} y = 0 \]

12842

\[ {} y^{\left (5\right )}+a y^{\prime \prime \prime \prime }-f = 0 \]

12843

\[ {} x y^{\left (5\right )}-m n y^{\prime \prime \prime \prime }+a x y = 0 \]

12844

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

12845

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

12846

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

12847

\[ {} x^{10} y^{\left (5\right )}-a y = 0 \]

12848

\[ {} x^{{5}/{2}} y^{\left (5\right )}-a y = 0 \]

12849

\[ {} \left (x -a \right )^{5} \left (x -b \right )^{5} y^{\left (5\right )}-c y = 0 \]

13061

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

13062

\[ {} y^{\prime \prime \prime }+y y^{\prime \prime }-{y^{\prime }}^{2}+1 = 0 \]

13063

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

13064

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

13065

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

13066

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

13067

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

13068

\[ {} 15 {y^{\prime }}^{3}-18 y y^{\prime } y^{\prime \prime }+4 y^{2} y^{\prime \prime \prime } = 0 \]

13069

\[ {} 40 {y^{\prime }}^{3}-45 y y^{\prime } y^{\prime \prime }+9 y^{2} y^{\prime \prime \prime } = 0 \]

13070

\[ {} 2 y^{\prime } y^{\prime \prime \prime }-3 {y^{\prime }}^{2} = 0 \]

13071

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

13072

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

13073

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

13074

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

13075

\[ {} 3 y^{\prime \prime } y^{\prime \prime \prime \prime }-5 {y^{\prime \prime \prime }}^{2} = 0 \]

13076

\[ {} 9 {y^{\prime \prime }}^{2} y^{\left (5\right )}-45 y^{\prime \prime } y^{\prime \prime \prime } y^{\prime \prime \prime \prime }+40 y^{\prime \prime \prime } = 0 \]

13078

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

14202

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

14203

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

14204

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

14205

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

14206

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

14207

\[ {} y^{\prime \prime \prime }-6 y^{\prime \prime }+9 y^{\prime } = 0 \]

14208

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

14209

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

14210

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

14212

\[ {} y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y = 2 \,{\mathrm e}^{-x}-x^{2} {\mathrm e}^{-x} \]

14215

\[ {} y^{\prime \prime \prime }-3 y^{\prime \prime }-y^{\prime }+3 y = x^{2} \]

14217

\[ {} y^{\prime \prime \prime }-4 y^{\prime \prime }+5 y^{\prime }-2 y = x \]

14224

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

14225

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

14226

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

14228

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

14229

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

14230

\[ {} 2 y+2 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime } = 10 x +\frac {10}{x} \]

14234

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

14236

\[ {} -4 y^{\prime }+y^{\prime \prime \prime } = -3 \,{\mathrm e}^{2 x}+x^{2} \]

14237

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

14238

\[ {} y+3 x y^{\prime }+9 x^{2} y^{\prime \prime }+6 x^{3} y^{\prime \prime \prime }+x^{4} y^{\prime \prime \prime \prime } = \left (\ln \left (x \right )+1\right )^{2} \]

14239

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

14242

\[ {} -2 y+5 y^{\prime }-3 y^{\prime \prime }-y^{\prime \prime \prime }+y^{\prime \prime \prime \prime } = {\mathrm e}^{3 x} \]

14244

\[ {} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-x y^{\prime }+y = \frac {1}{x} \]

14245

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

14270

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

14278

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

14279

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

14280

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

14283

\[ {} \left (x^{3}-x \right ) y^{\prime \prime \prime }+\left (8 x^{2}-3\right ) y^{\prime \prime }+14 x y^{\prime }+4 y = 0 \]

14284

\[ {} 2 x^{3} y y^{\prime \prime \prime }+6 x^{3} y^{\prime } y^{\prime \prime }+18 x^{2} y y^{\prime \prime }+18 x^{2} {y^{\prime }}^{2}+36 y y^{\prime } x +6 y^{2} = 0 \]

14287

\[ {} x^{2} y^{\prime \prime \prime }-5 x y^{\prime \prime }+\left (4 x^{4}+5\right ) y^{\prime }-8 x^{3} y = 0 \]

14296

\[ {} 6 y+18 x y^{\prime }+9 x^{2} y^{\prime \prime }+\left (x^{3}+1\right ) y^{\prime \prime \prime } = 0 \]

14303

\[ {} y^{\prime }+8 x y^{\prime \prime }+4 x^{2} y^{\prime \prime \prime } = 0 \]

14458

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

14459

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

14460

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

14461

\[ {} x^{\prime \prime \prime }-x^{\prime }-8 x = 0 \]

14462

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

14463

\[ {} x^{\prime \prime \prime }-8 x = 0 \]

14464

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

14536

\[ {} y^{\prime \prime \prime }-2 y^{\prime \prime }-4 y^{\prime }+8 y = 0 \]

14537

\[ {} y^{\prime \prime \prime }-3 y^{\prime \prime }-4 y^{\prime }+12 y = 0 \]

14538

\[ {} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-10 x y^{\prime }-8 y = 0 \]

14549

\[ {} x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 x y^{\prime }-6 y = 0 \]

14678

\[ {} y^{\prime \prime \prime }-6 y^{\prime \prime }+5 y^{\prime }+12 y = 0 \]

14679

\[ {} x^{3} y^{\prime \prime \prime }-4 x^{2} y^{\prime \prime }+8 x y^{\prime }-8 y = 0 \]

14692

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

14693

\[ {} y^{\prime \prime \prime }-6 y^{\prime \prime }+5 y^{\prime }+12 y = 0 \]

14700

\[ {} y^{\prime \prime \prime }-5 y^{\prime \prime }+7 y^{\prime }-3 y = 0 \]

14701

\[ {} 4 y^{\prime \prime \prime }+4 y^{\prime \prime }-7 y^{\prime }+2 y = 0 \]

14702

\[ {} y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y = 0 \]

14703

\[ {} y^{\prime \prime \prime }+4 y^{\prime \prime }+5 y^{\prime }+6 y = 0 \]

14704

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

14705

\[ {} y^{\prime \prime \prime \prime }+8 y^{\prime \prime }+16 y = 0 \]