2.228   ODE No. 228

  1. Problem in Latex
  2. Mathematica input
  3. Maple input

\[ (4 y(x)+11 x-11) y'(x)-25 y(x)-8 x+62=0 \] Mathematica : cpu = 0.30765 (sec), leaf count = 1677

\[\left \{\left \{y(x)\to \frac {1}{4} \left (\frac {3 (9 x-1)}{\frac {\sqrt [3]{-6561 \cosh \left (\frac {3 c_1}{4}\right ) x^4-6561 \sinh \left (\frac {3 c_1}{4}\right ) x^4+2916 \cosh \left (\frac {3 c_1}{4}\right ) x^3+2916 \sinh \left (\frac {3 c_1}{4}\right ) x^3+162 \cosh \left (\frac {3 c_1}{8}\right ) x^2-486 \cosh \left (\frac {3 c_1}{4}\right ) x^2+162 \sinh \left (\frac {3 c_1}{8}\right ) x^2-486 \sinh \left (\frac {3 c_1}{4}\right ) x^2-36 \cosh \left (\frac {3 c_1}{8}\right ) x+36 \cosh \left (\frac {3 c_1}{4}\right ) x-36 \sinh \left (\frac {3 c_1}{8}\right ) x+36 \sinh \left (\frac {3 c_1}{4}\right ) x+2 \cosh \left (\frac {3 c_1}{8}\right )-\cosh \left (\frac {3 c_1}{4}\right )+2 \sinh \left (\frac {3 c_1}{8}\right )-\sinh \left (\frac {3 c_1}{4}\right )+\sqrt {(1-9 x)^2 \left (9 x (9 x-2) \cosh \left (\frac {3 c_1}{16}\right )+\left (81 x^2-18 x+2\right ) \sinh \left (\frac {3 c_1}{16}\right )\right ){}^3 \left (\cosh \left (\frac {15 c_1}{16}\right )+\sinh \left (\frac {15 c_1}{16}\right )\right )}-1}}{\cosh \left (\frac {3 c_1}{8}\right ) (1-9 x)^2+\sinh \left (\frac {3 c_1}{8}\right ) (1-9 x)^2-1}+1-\frac {1}{\sqrt [3]{-6561 \cosh \left (\frac {3 c_1}{4}\right ) x^4-6561 \sinh \left (\frac {3 c_1}{4}\right ) x^4+2916 \cosh \left (\frac {3 c_1}{4}\right ) x^3+2916 \sinh \left (\frac {3 c_1}{4}\right ) x^3+162 \cosh \left (\frac {3 c_1}{8}\right ) x^2-486 \cosh \left (\frac {3 c_1}{4}\right ) x^2+162 \sinh \left (\frac {3 c_1}{8}\right ) x^2-486 \sinh \left (\frac {3 c_1}{4}\right ) x^2-36 \cosh \left (\frac {3 c_1}{8}\right ) x+36 \cosh \left (\frac {3 c_1}{4}\right ) x-36 \sinh \left (\frac {3 c_1}{8}\right ) x+36 \sinh \left (\frac {3 c_1}{4}\right ) x+2 \cosh \left (\frac {3 c_1}{8}\right )-\cosh \left (\frac {3 c_1}{4}\right )+2 \sinh \left (\frac {3 c_1}{8}\right )-\sinh \left (\frac {3 c_1}{4}\right )+\sqrt {(1-9 x)^2 \left (9 x (9 x-2) \cosh \left (\frac {3 c_1}{16}\right )+\left (81 x^2-18 x+2\right ) \sinh \left (\frac {3 c_1}{16}\right )\right ){}^3 \left (\cosh \left (\frac {15 c_1}{16}\right )+\sinh \left (\frac {15 c_1}{16}\right )\right )}-1}}}-11 (x-1)\right )\right \},\left \{y(x)\to \frac {1}{4} \left (\frac {6 (9 x-1)}{\frac {i \left (i+\sqrt {3}\right ) \sqrt [3]{-6561 \cosh \left (\frac {3 c_1}{4}\right ) x^4-6561 \sinh \left (\frac {3 c_1}{4}\right ) x^4+2916 \cosh \left (\frac {3 c_1}{4}\right ) x^3+2916 \sinh \left (\frac {3 c_1}{4}\right ) x^3+162 \cosh \left (\frac {3 c_1}{8}\right ) x^2-486 \cosh \left (\frac {3 c_1}{4}\right ) x^2+162 \sinh \left (\frac {3 c_1}{8}\right ) x^2-486 \sinh \left (\frac {3 c_1}{4}\right ) x^2-36 \cosh \left (\frac {3 c_1}{8}\right ) x+36 \cosh \left (\frac {3 c_1}{4}\right ) x-36 \sinh \left (\frac {3 c_1}{8}\right ) x+36 \sinh \left (\frac {3 c_1}{4}\right ) x+2 \cosh \left (\frac {3 c_1}{8}\right )-\cosh \left (\frac {3 c_1}{4}\right )+2 \sinh \left (\frac {3 c_1}{8}\right )-\sinh \left (\frac {3 c_1}{4}\right )+\sqrt {(1-9 x)^2 \left (9 x (9 x-2) \cosh \left (\frac {3 c_1}{16}\right )+\left (81 x^2-18 x+2\right ) \sinh \left (\frac {3 c_1}{16}\right )\right ){}^3 \left (\cosh \left (\frac {15 c_1}{16}\right )+\sinh \left (\frac {15 c_1}{16}\right )\right )}-1}}{\cosh \left (\frac {3 c_1}{8}\right ) (1-9 x)^2+\sinh \left (\frac {3 c_1}{8}\right ) (1-9 x)^2-1}+2+\frac {1+i \sqrt {3}}{\sqrt [3]{-6561 \cosh \left (\frac {3 c_1}{4}\right ) x^4-6561 \sinh \left (\frac {3 c_1}{4}\right ) x^4+2916 \cosh \left (\frac {3 c_1}{4}\right ) x^3+2916 \sinh \left (\frac {3 c_1}{4}\right ) x^3+162 \cosh \left (\frac {3 c_1}{8}\right ) x^2-486 \cosh \left (\frac {3 c_1}{4}\right ) x^2+162 \sinh \left (\frac {3 c_1}{8}\right ) x^2-486 \sinh \left (\frac {3 c_1}{4}\right ) x^2-36 \cosh \left (\frac {3 c_1}{8}\right ) x+36 \cosh \left (\frac {3 c_1}{4}\right ) x-36 \sinh \left (\frac {3 c_1}{8}\right ) x+36 \sinh \left (\frac {3 c_1}{4}\right ) x+2 \cosh \left (\frac {3 c_1}{8}\right )-\cosh \left (\frac {3 c_1}{4}\right )+2 \sinh \left (\frac {3 c_1}{8}\right )-\sinh \left (\frac {3 c_1}{4}\right )+\sqrt {(1-9 x)^2 \left (9 x (9 x-2) \cosh \left (\frac {3 c_1}{16}\right )+\left (81 x^2-18 x+2\right ) \sinh \left (\frac {3 c_1}{16}\right )\right ){}^3 \left (\cosh \left (\frac {15 c_1}{16}\right )+\sinh \left (\frac {15 c_1}{16}\right )\right )}-1}}}-11 (x-1)\right )\right \},\left \{y(x)\to \frac {1}{4} \left (\frac {6 (9 x-1)}{-\frac {i \left (-i+\sqrt {3}\right ) \sqrt [3]{-6561 \cosh \left (\frac {3 c_1}{4}\right ) x^4-6561 \sinh \left (\frac {3 c_1}{4}\right ) x^4+2916 \cosh \left (\frac {3 c_1}{4}\right ) x^3+2916 \sinh \left (\frac {3 c_1}{4}\right ) x^3+162 \cosh \left (\frac {3 c_1}{8}\right ) x^2-486 \cosh \left (\frac {3 c_1}{4}\right ) x^2+162 \sinh \left (\frac {3 c_1}{8}\right ) x^2-486 \sinh \left (\frac {3 c_1}{4}\right ) x^2-36 \cosh \left (\frac {3 c_1}{8}\right ) x+36 \cosh \left (\frac {3 c_1}{4}\right ) x-36 \sinh \left (\frac {3 c_1}{8}\right ) x+36 \sinh \left (\frac {3 c_1}{4}\right ) x+2 \cosh \left (\frac {3 c_1}{8}\right )-\cosh \left (\frac {3 c_1}{4}\right )+2 \sinh \left (\frac {3 c_1}{8}\right )-\sinh \left (\frac {3 c_1}{4}\right )+\sqrt {(1-9 x)^2 \left (9 x (9 x-2) \cosh \left (\frac {3 c_1}{16}\right )+\left (81 x^2-18 x+2\right ) \sinh \left (\frac {3 c_1}{16}\right )\right ){}^3 \left (\cosh \left (\frac {15 c_1}{16}\right )+\sinh \left (\frac {15 c_1}{16}\right )\right )}-1}}{\cosh \left (\frac {3 c_1}{8}\right ) (1-9 x)^2+\sinh \left (\frac {3 c_1}{8}\right ) (1-9 x)^2-1}+2+\frac {1-i \sqrt {3}}{\sqrt [3]{-6561 \cosh \left (\frac {3 c_1}{4}\right ) x^4-6561 \sinh \left (\frac {3 c_1}{4}\right ) x^4+2916 \cosh \left (\frac {3 c_1}{4}\right ) x^3+2916 \sinh \left (\frac {3 c_1}{4}\right ) x^3+162 \cosh \left (\frac {3 c_1}{8}\right ) x^2-486 \cosh \left (\frac {3 c_1}{4}\right ) x^2+162 \sinh \left (\frac {3 c_1}{8}\right ) x^2-486 \sinh \left (\frac {3 c_1}{4}\right ) x^2-36 \cosh \left (\frac {3 c_1}{8}\right ) x+36 \cosh \left (\frac {3 c_1}{4}\right ) x-36 \sinh \left (\frac {3 c_1}{8}\right ) x+36 \sinh \left (\frac {3 c_1}{4}\right ) x+2 \cosh \left (\frac {3 c_1}{8}\right )-\cosh \left (\frac {3 c_1}{4}\right )+2 \sinh \left (\frac {3 c_1}{8}\right )-\sinh \left (\frac {3 c_1}{4}\right )+\sqrt {(1-9 x)^2 \left (9 x (9 x-2) \cosh \left (\frac {3 c_1}{16}\right )+\left (81 x^2-18 x+2\right ) \sinh \left (\frac {3 c_1}{16}\right )\right ){}^3 \left (\cosh \left (\frac {15 c_1}{16}\right )+\sinh \left (\frac {15 c_1}{16}\right )\right )}-1}}}-11 (x-1)\right )\right \}\right \}\]

Maple : cpu = 0.405 (sec), leaf count = 271

\[ \left \{ y \left ( x \right ) ={1 \left ( \left ( -76\,x+28 \right ) \sqrt [3]{64-8748\, \left ( 9\,x-1 \right ) ^{2}{\it \_C1}+108\,\sqrt {43046721}\sqrt { \left ( x-1/9 \right ) ^{2}{\it \_C1}\, \left ( -{\frac {32}{177147}}+ \left ( x-1/9 \right ) ^{2}{\it \_C1} \right ) }}+4\, \left ( \left ( i \left ( 64-8748\, \left ( 9\,x-1 \right ) ^{2}{\it \_C1}+108\,\sqrt {43046721}\sqrt { \left ( x-1/9 \right ) ^{2}{\it \_C1}\, \left ( -{\frac {32}{177147}}+ \left ( x-1/9 \right ) ^{2}{\it \_C1} \right ) } \right ) ^{2/3}-16\,i \right ) \sqrt {3}- \left ( 64-8748\, \left ( 9\,x-1 \right ) ^{2}{\it \_C1}+108\,\sqrt {43046721}\sqrt { \left ( x-1/9 \right ) ^{2}{\it \_C1}\, \left ( -{\frac {32}{177147}}+ \left ( x-1/9 \right ) ^{2}{\it \_C1} \right ) } \right ) ^{2/3}-16 \right ) \left ( x+1/2 \right ) \right ) \left ( 8\,\sqrt [3]{64-8748\, \left ( 9\,x-1 \right ) ^{2}{\it \_C1}+108\,\sqrt {43046721}\sqrt { \left ( x-1/9 \right ) ^{2}{\it \_C1}\, \left ( -{\frac {32}{177147}}+ \left ( x-1/9 \right ) ^{2}{\it \_C1} \right ) }}+ \left ( i \left ( 64-8748\, \left ( 9\,x-1 \right ) ^{2}{\it \_C1}+108\,\sqrt {43046721}\sqrt { \left ( x-1/9 \right ) ^{2}{\it \_C1}\, \left ( -{\frac {32}{177147}}+ \left ( x-1/9 \right ) ^{2}{\it \_C1} \right ) } \right ) ^{{\frac {2}{3}}}-16\,i \right ) \sqrt {3}- \left ( 64-8748\, \left ( 9\,x-1 \right ) ^{2}{\it \_C1}+108\,\sqrt {43046721}\sqrt { \left ( x-1/9 \right ) ^{2}{\it \_C1}\, \left ( -{\frac {32}{177147}}+ \left ( x-1/9 \right ) ^{2}{\it \_C1} \right ) } \right ) ^{{\frac {2}{3}}}-16 \right ) ^{-1}} \right \} \]