ODE
\[ y'''(x)+y''(x)+2 y'(x)+4 y(x)=\sin (2 x) \] ODE Classification
[[_3rd_order, _linear, _nonhomogeneous]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.291977 (sec), leaf count = 1185
\[\left \{\left \{y(x)\to e^{x \text {Root}\left [\text {$\#$1}^3+\text {$\#$1}^2+2 \text {$\#$1}+4\& ,1\right ]} c_1+e^{x \text {Root}\left [\text {$\#$1}^3+\text {$\#$1}^2+2 \text {$\#$1}+4\& ,2\right ]} c_2+e^{x \text {Root}\left [\text {$\#$1}^3+\text {$\#$1}^2+2 \text {$\#$1}+4\& ,3\right ]} c_3+\frac {8 \left (\text {Root}\left [\text {$\#$1}^3+\text {$\#$1}^2+2 \text {$\#$1}+4\& ,2\right ] \text {Root}\left [\text {$\#$1}^3+\text {$\#$1}^2+2 \text {$\#$1}+4\& ,3\right ] \left (-252+\left (-70+26 \text {Root}\left [\text {$\#$1}^3+\text {$\#$1}^2+2 \text {$\#$1}+4\& ,1\right ]+\text {Root}\left [\text {$\#$1}^3+\text {$\#$1}^2+2 \text {$\#$1}+4\& ,1\right ]^2\right ) \text {Root}\left [\text {$\#$1}^3+\text {$\#$1}^2+2 \text {$\#$1}+4\& ,3\right ]\right )+2 \left (166-\left (64+118 \text {Root}\left [\text {$\#$1}^3+\text {$\#$1}^2+2 \text {$\#$1}+4\& ,1\right ]+3 \text {Root}\left [\text {$\#$1}^3+\text {$\#$1}^2+2 \text {$\#$1}+4\& ,1\right ]^2\right ) \text {Root}\left [\text {$\#$1}^3+\text {$\#$1}^2+2 \text {$\#$1}+4\& ,3\right ]+\left (-84-15 \text {Root}\left [\text {$\#$1}^3+\text {$\#$1}^2+2 \text {$\#$1}+4\& ,1\right ]+5 \text {Root}\left [\text {$\#$1}^3+\text {$\#$1}^2+2 \text {$\#$1}+4\& ,1\right ]^2\right ) \text {Root}\left [\text {$\#$1}^3+\text {$\#$1}^2+2 \text {$\#$1}+4\& ,3\right ]^2\right )+2 \text {Root}\left [\text {$\#$1}^3+\text {$\#$1}^2+2 \text {$\#$1}+4\& ,2\right ]^2 \left (-26-3 \text {Root}\left [\text {$\#$1}^3+\text {$\#$1}^2+2 \text {$\#$1}+4\& ,3\right ]+18 \text {Root}\left [\text {$\#$1}^3+\text {$\#$1}^2+2 \text {$\#$1}+4\& ,3\right ]^2+\text {Root}\left [\text {$\#$1}^3+\text {$\#$1}^2+2 \text {$\#$1}+4\& ,1\right ] \left (10+25 \text {Root}\left [\text {$\#$1}^3+\text {$\#$1}^2+2 \text {$\#$1}+4\& ,3\right ]+8 \text {Root}\left [\text {$\#$1}^3+\text {$\#$1}^2+2 \text {$\#$1}+4\& ,3\right ]^2\right )\right )\right ) \cos (2 x)+\left (\text {Root}\left [\text {$\#$1}^3+\text {$\#$1}^2+2 \text {$\#$1}+4\& ,2\right ] \left (128+24 \text {Root}\left [\text {$\#$1}^3+\text {$\#$1}^2+2 \text {$\#$1}+4\& ,3\right ]-5 \left (-24-50 \text {Root}\left [\text {$\#$1}^3+\text {$\#$1}^2+2 \text {$\#$1}+4\& ,1\right ]+3 \text {Root}\left [\text {$\#$1}^3+\text {$\#$1}^2+2 \text {$\#$1}+4\& ,1\right ]^2\right ) \text {Root}\left [\text {$\#$1}^3+\text {$\#$1}^2+2 \text {$\#$1}+4\& ,3\right ]^2\right )+4 \left (24+\left (116-30 \text {Root}\left [\text {$\#$1}^3+\text {$\#$1}^2+2 \text {$\#$1}+4\& ,1\right ]+23 \text {Root}\left [\text {$\#$1}^3+\text {$\#$1}^2+2 \text {$\#$1}+4\& ,1\right ]^2\right ) \text {Root}\left [\text {$\#$1}^3+\text {$\#$1}^2+2 \text {$\#$1}+4\& ,3\right ]+\left (36+6 \text {Root}\left [\text {$\#$1}^3+\text {$\#$1}^2+2 \text {$\#$1}+4\& ,1\right ]+11 \text {Root}\left [\text {$\#$1}^3+\text {$\#$1}^2+2 \text {$\#$1}+4\& ,1\right ]^2\right ) \text {Root}\left [\text {$\#$1}^3+\text {$\#$1}^2+2 \text {$\#$1}+4\& ,3\right ]^2\right )+\text {Root}\left [\text {$\#$1}^3+\text {$\#$1}^2+2 \text {$\#$1}+4\& ,2\right ]^2 \left (\text {Root}\left [\text {$\#$1}^3+\text {$\#$1}^2+2 \text {$\#$1}+4\& ,1\right ] \left (-88+96 \text {Root}\left [\text {$\#$1}^3+\text {$\#$1}^2+2 \text {$\#$1}+4\& ,3\right ]+25 \text {Root}\left [\text {$\#$1}^3+\text {$\#$1}^2+2 \text {$\#$1}+4\& ,3\right ]^2\right )+4 \left (52+25 \text {Root}\left [\text {$\#$1}^3+\text {$\#$1}^2+2 \text {$\#$1}+4\& ,3\right ]+51 \text {Root}\left [\text {$\#$1}^3+\text {$\#$1}^2+2 \text {$\#$1}+4\& ,3\right ]^2\right )\right )\right ) \sin (2 x)}{\text {Root}\left [\text {$\#$1}^3+\text {$\#$1}^2+2 \text {$\#$1}+4\& ,1\right ]^2 \left (\text {Root}\left [\text {$\#$1}^3+\text {$\#$1}^2+2 \text {$\#$1}+4\& ,1\right ]-\text {Root}\left [\text {$\#$1}^3+\text {$\#$1}^2+2 \text {$\#$1}+4\& ,2\right ]\right ) \text {Root}\left [\text {$\#$1}^3+\text {$\#$1}^2+2 \text {$\#$1}+4\& ,2\right ] \left (4+\text {Root}\left [\text {$\#$1}^3+\text {$\#$1}^2+2 \text {$\#$1}+4\& ,2\right ]^2\right ) \left (\text {Root}\left [\text {$\#$1}^3+\text {$\#$1}^2+2 \text {$\#$1}+4\& ,1\right ]-\text {Root}\left [\text {$\#$1}^3+\text {$\#$1}^2+2 \text {$\#$1}+4\& ,3\right ]\right ) \left (\text {Root}\left [\text {$\#$1}^3+\text {$\#$1}^2+2 \text {$\#$1}+4\& ,2\right ]-\text {Root}\left [\text {$\#$1}^3+\text {$\#$1}^2+2 \text {$\#$1}+4\& ,3\right ]\right ) \left ((1-2 i)+\text {Root}\left [\text {$\#$1}^3+\text {$\#$1}^2+2 \text {$\#$1}+4\& ,2\right ]+\text {Root}\left [\text {$\#$1}^3+\text {$\#$1}^2+2 \text {$\#$1}+4\& ,3\right ]\right ) \left ((1+2 i)+\text {Root}\left [\text {$\#$1}^3+\text {$\#$1}^2+2 \text {$\#$1}+4\& ,2\right ]+\text {Root}\left [\text {$\#$1}^3+\text {$\#$1}^2+2 \text {$\#$1}+4\& ,3\right ]\right ) \left (-2+\text {Root}\left [\text {$\#$1}^3+\text {$\#$1}^2+2 \text {$\#$1}+4\& ,2\right ]^2+2 \text {Root}\left [\text {$\#$1}^3+\text {$\#$1}^2+2 \text {$\#$1}+4\& ,1\right ] \text {Root}\left [\text {$\#$1}^3+\text {$\#$1}^2+2 \text {$\#$1}+4\& ,3\right ]\right ) \left (4+\text {Root}\left [\text {$\#$1}^3+\text {$\#$1}^2+2 \text {$\#$1}+4\& ,3\right ]^2\right )}\right \}\right \}\]
Maple ✓
cpu = 0.714 (sec), leaf count = 1277
\[ \left \{ y \left ( x \right ) ={\frac {1}{207500\,\sqrt [3]{46+3\,\sqrt {3}\sqrt {83}}+ \left ( -24900\,\sqrt {3}\sqrt {83}+485550 \right ) \left ( 46+3\,\sqrt {3}\sqrt {83} \right ) ^{{\frac {2}{3}}}+2801250+ \left ( -45816\,\sqrt {3}\sqrt {83}+723262 \right ) \left ( 46+3\,\sqrt {3}\sqrt {83} \right ) ^{{\frac {4}{3}}}} \left ( -207500\,{{\rm e}^{-{\frac { \left ( 3\,\sqrt {249} \left ( 46+3\,\sqrt {249} \right ) ^{2/3}-46\, \left ( 46+3\,\sqrt {249} \right ) ^{2/3}-25\,\sqrt [3]{46+3\,\sqrt {249}}+50 \right ) x}{150}}}}\cos \left ( {\frac {23\,\sqrt [3]{46+3\,\sqrt {3}\sqrt {83}}x \left ( \left ( \sqrt {3}-{\frac {9\,\sqrt {83}}{46}} \right ) \sqrt [3]{46+3\,\sqrt {3}\sqrt {83}}-{\frac {25\,\sqrt {3}}{46}} \right ) }{75}} \right ) \left ( \sqrt [3]{46+3\,\sqrt {3}\sqrt {83}}+ \left ( -{\frac {3\,\sqrt {3}\sqrt {83}}{25}}+{\frac {117}{50}} \right ) \left ( 46+3\,\sqrt {3}\sqrt {83} \right ) ^{2/3}+{\frac {27}{2}}+ \left ( -{\frac {138\,\sqrt {3}\sqrt {83}}{625}}+{\frac {4357}{1250}} \right ) \left ( 46+3\,\sqrt {3}\sqrt {83} \right ) ^{4/3} \right ) \int \!{\frac {3\,\sqrt {83}\sin \left ( 2\,x \right ) }{4150} \left ( \left ( {\frac {25\,\sqrt {3}\sqrt [3]{46+3\,\sqrt {3}\sqrt {83}}}{9}}-{\frac { \left ( 46\,\sqrt {3}-9\,\sqrt {83} \right ) \left ( 46+3\,\sqrt {3}\sqrt {83} \right ) ^{2/3}}{9}} \right ) \cos \left ( {\frac {23\,\sqrt [3]{46+3\,\sqrt {3}\sqrt {83}}x \left ( \left ( \sqrt {3}-{\frac {9\,\sqrt {83}}{46}} \right ) \sqrt [3]{46+3\,\sqrt {3}\sqrt {83}}-{\frac {25\,\sqrt {3}}{46}} \right ) }{75}} \right ) + \left ( \left ( \sqrt {249}-{\frac {46}{3}} \right ) \left ( 46+3\,\sqrt {249} \right ) ^{2/3}-{\frac {25\,\sqrt [3]{46+3\,\sqrt {249}}}{3}} \right ) \sin \left ( {\frac {23\,\sqrt [3]{46+3\,\sqrt {3}\sqrt {83}}x \left ( \left ( \sqrt {3}-{\frac {9\,\sqrt {83}}{46}} \right ) \sqrt [3]{46+3\,\sqrt {3}\sqrt {83}}-{\frac {25\,\sqrt {3}}{46}} \right ) }{75}} \right ) \right ) {{\rm e}^{{\frac { \left ( 3\,\sqrt {249} \left ( 46+3\,\sqrt {249} \right ) ^{2/3}-46\, \left ( 46+3\,\sqrt {249} \right ) ^{2/3}-25\,\sqrt [3]{46+3\,\sqrt {249}}+50 \right ) x}{150}}}}}\,{\rm d}x-207500\,{{\rm e}^{-{\frac { \left ( 3\,\sqrt {249} \left ( 46+3\,\sqrt {249} \right ) ^{2/3}-46\, \left ( 46+3\,\sqrt {249} \right ) ^{2/3}-25\,\sqrt [3]{46+3\,\sqrt {249}}+50 \right ) x}{150}}}}\sin \left ( {\frac {23\,\sqrt [3]{46+3\,\sqrt {3}\sqrt {83}}x \left ( \left ( \sqrt {3}-{\frac {9\,\sqrt {83}}{46}} \right ) \sqrt [3]{46+3\,\sqrt {3}\sqrt {83}}-{\frac {25\,\sqrt {3}}{46}} \right ) }{75}} \right ) \left ( \sqrt [3]{46+3\,\sqrt {3}\sqrt {83}}+ \left ( -{\frac {3\,\sqrt {3}\sqrt {83}}{25}}+{\frac {117}{50}} \right ) \left ( 46+3\,\sqrt {3}\sqrt {83} \right ) ^{2/3}+{\frac {27}{2}}+ \left ( -{\frac {138\,\sqrt {3}\sqrt {83}}{625}}+{\frac {4357}{1250}} \right ) \left ( 46+3\,\sqrt {3}\sqrt {83} \right ) ^{4/3} \right ) \int \!{\frac {\sqrt {83}\sin \left ( 2\,x \right ) }{498}{{\rm e}^{{\frac { \left ( 3\,\sqrt {249} \left ( 46+3\,\sqrt {249} \right ) ^{2/3}-46\, \left ( 46+3\,\sqrt {249} \right ) ^{2/3}-25\,\sqrt [3]{46+3\,\sqrt {249}}+50 \right ) x}{150}}}} \left ( \left ( \left ( -{\frac {9\,\sqrt {249}}{25}}+{\frac {138}{25}} \right ) \left ( 46+3\,\sqrt {249} \right ) ^{2/3}+3\,\sqrt [3]{46+3\,\sqrt {249}} \right ) \cos \left ( {\frac {23\,\sqrt [3]{46+3\,\sqrt {3}\sqrt {83}}x \left ( \left ( \sqrt {3}-{\frac {9\,\sqrt {83}}{46}} \right ) \sqrt [3]{46+3\,\sqrt {3}\sqrt {83}}-{\frac {25\,\sqrt {3}}{46}} \right ) }{75}} \right ) +\sin \left ( {\frac {23\,\sqrt [3]{46+3\,\sqrt {3}\sqrt {83}}x \left ( \left ( \sqrt {3}-{\frac {9\,\sqrt {83}}{46}} \right ) \sqrt [3]{46+3\,\sqrt {3}\sqrt {83}}-{\frac {25\,\sqrt {3}}{46}} \right ) }{75}} \right ) \left ( \sqrt {3}\sqrt [3]{46+3\,\sqrt {3}\sqrt {83}}-{\frac { \left ( 46\,\sqrt {3}-9\,\sqrt {83} \right ) \left ( 46+3\,\sqrt {3}\sqrt {83} \right ) ^{2/3}}{25}} \right ) \right ) }\,{\rm d}x+ \left ( -3750\,\sqrt {83}\sqrt {3} \left ( \cos \left ( 2\,x \right ) -1/6\,\sin \left ( 2\,x \right ) \right ) \sqrt [3]{46+3\,\sqrt {3}\sqrt {83}}+ \left ( 6900\,\sqrt {3}\sqrt {83}\cos \left ( 2\,x \right ) -525\,\sqrt {3}\sqrt {83}\sin \left ( 2\,x \right ) -112050\,\cos \left ( 2\,x \right ) +18675\,\sin \left ( 2\,x \right ) \right ) \left ( 46+3\,\sqrt {3}\sqrt {83} \right ) ^{{\frac {2}{3}}}-4357\,\sin \left ( 2\,x \right ) \left ( \sqrt {3}\sqrt {83}-{\frac {68724}{4357}} \right ) \left ( 46+3\,\sqrt {3}\sqrt {83} \right ) ^{4/3} \right ) {{\rm e}^{-{\frac {x \left ( 3\,\sqrt {3}\sqrt {83} \left ( 46+3\,\sqrt {3}\sqrt {83} \right ) ^{2/3}-3\,\sqrt {249} \left ( 46+3\,\sqrt {249} \right ) ^{2/3}-46\, \left ( 46+3\,\sqrt {3}\sqrt {83} \right ) ^{2/3}+46\, \left ( 46+3\,\sqrt {249} \right ) ^{2/3}-25\,\sqrt [3]{46+3\,\sqrt {3}\sqrt {83}}+25\,\sqrt [3]{46+3\,\sqrt {249}} \right ) }{75}}}}+207500\, \left ( {\it \_C2}\,{{\rm e}^{-{\frac { \left ( 3\,\sqrt {249} \left ( 46+3\,\sqrt {249} \right ) ^{2/3}-46\, \left ( 46+3\,\sqrt {249} \right ) ^{2/3}-25\,\sqrt [3]{46+3\,\sqrt {249}}+50 \right ) x}{150}}}}\cos \left ( {\frac { \left ( 46\,\sqrt {3}-9\,\sqrt {83} \right ) x \left ( 46+3\,\sqrt {3}\sqrt {83} \right ) ^{2/3}}{150}}-1/6\,\sqrt [3]{46+3\,\sqrt {3}\sqrt {83}}\sqrt {3}x \right ) +{\it \_C3}\,{{\rm e}^{-{\frac { \left ( 3\,\sqrt {249} \left ( 46+3\,\sqrt {249} \right ) ^{2/3}-46\, \left ( 46+3\,\sqrt {249} \right ) ^{2/3}-25\,\sqrt [3]{46+3\,\sqrt {249}}+50 \right ) x}{150}}}}\sin \left ( {\frac { \left ( 46\,\sqrt {3}-9\,\sqrt {83} \right ) x \left ( 46+3\,\sqrt {3}\sqrt {83} \right ) ^{2/3}}{150}}-1/6\,\sqrt [3]{46+3\,\sqrt {3}\sqrt {83}}\sqrt {3}x \right ) +{\it \_C1}\,{{\rm e}^{{\frac { \left ( 3\,\sqrt {249} \left ( 46+3\,\sqrt {249} \right ) ^{2/3}-46\, \left ( 46+3\,\sqrt {249} \right ) ^{2/3}-25\,\sqrt [3]{46+3\,\sqrt {249}}-25 \right ) x}{75}}}} \right ) \left ( \sqrt [3]{46+3\,\sqrt {3}\sqrt {83}}+ \left ( -{\frac {3\,\sqrt {3}\sqrt {83}}{25}}+{\frac {117}{50}} \right ) \left ( 46+3\,\sqrt {3}\sqrt {83} \right ) ^{2/3}+{\frac {27}{2}}+ \left ( -{\frac {138\,\sqrt {3}\sqrt {83}}{625}}+{\frac {4357}{1250}} \right ) \left ( 46+3\,\sqrt {3}\sqrt {83} \right ) ^{4/3} \right ) \right ) } \right \} \] Mathematica raw input
DSolve[4*y[x] + 2*y'[x] + y''[x] + y'''[x] == Sin[2*x],y[x],x]
Mathematica raw output
{{y[x] -> E^(x*Root[4 + 2*#1 + #1^2 + #1^3 & , 1, 0])*C[1] + E^(x*Root[4 + 2*#1 + #1^2 + #1^3 & , 2, 0])*C[2] + E^(x*Root[4 + 2*#1 + #1^2 + #1^3 & , 3, 0])*C[3] + (8*Cos[2*x]*(Root[4 + 2*#1 + #1^2 + #1^3 & , 2, 0]*Root[4 + 2*#1 + #1^2 + #1^3 & , 3, 0]*(-252 + (-70 + 26*Root[4 + 2*#1 + #1^2 + #1^3 & , 1, 0] + Root[4 + 2*#1 + #1^2 + #1^3 & , 1, 0]^2)*Root[4 + 2*#1 + #1^2 + #1^3 & , 3, 0]) + 2*(166 - (64 + 118*Root[4 + 2*#1 + #1^2 + #1^3 & , 1, 0] + 3*Root[4 + 2*#1 + #1^2 + #1^3 & , 1, 0]^2)*Root[4 + 2*#1 + #1^2 + #1^3 & , 3, 0] + (-84 - 15*Root[4 + 2*#1 + #1^2 + #1^3 & , 1, 0] + 5*Root[4 + 2*#1 + #1^2 + #1^3 & , 1, 0]^2)*Root[4 + 2*#1 + #1^2 + #1^3 & , 3, 0]^2) + 2*Root[4 + 2*#1 + #1^2 + #1^3 & , 2, 0]^2*(-26 - 3*Root[4 + 2*#1 + #1^2 + #1^3 & , 3, 0] + 18*Root[4 + 2*#1 + #1^2 + #1^3 & , 3, 0]^2 + Root[4 + 2*#1 + #1^2 + #1^3 & , 1, 0]*(10 + 25*Root[4 + 2*#1 + #1^2 + #1^3 & , 3, 0] + 8*Root[4 + 2*#1 + #1^2 + #1^3 & , 3, 0]^2))) + (Root[4 + 2*#1 + #1^2 + #1^3 & , 2, 0]*(128 + 24*Root[4 + 2*#1 + #1^2 + #1^3 & , 3, 0] - 5*(-24 - 50*Root[4 + 2*#1 + #1^2 + #1^3 & , 1, 0] + 3*Root[4 + 2*#1 + #1^2 + #1^3 & , 1, 0]^2)*Root[4 + 2*#1 + #1^2 + #1^3 & , 3, 0]^2) + 4*(24 + (116 - 30*Root[4 + 2*#1 + #1^2 + #1^3 & , 1, 0] + 23*Root[4 + 2*#1 + #1^2 + #1^3 & , 1, 0]^2)*Root[4 + 2*#1 + #1^2 + #1^3 & , 3, 0] + (36 + 6*Root[4 + 2*#1 + #1^2 + #1^3 & , 1, 0] + 11*Root[4 + 2*#1 + #1^2 + #1^3 & , 1, 0]^2)*Root[4 + 2*#1 + #1^2 + #1^3 & , 3, 0]^2) + Root[4 + 2*#1 + #1^2 + #1^3 & , 2, 0]^2*(Root[4 + 2*#1 + #1^2 + #1^3 & , 1, 0]*(-88 + 96*Root[4 + 2*#1 + #1^2 + #1^3 & , 3, 0] + 25*Root[4 + 2*#1 + #1^2 + #1^3 & , 3, 0]^2) + 4*(52 + 25*Root[4 + 2*#1 + #1^2 + #1^3 & , 3, 0] + 51*Root[4 + 2*#1 + #1^2 + #1^3 & , 3, 0]^2)))*Sin[2*x])/(Root[4 + 2*#1 + #1^2 + #1^3 & , 1, 0]^2*(Root[4 + 2*#1 + #1^2 + #1^3 & , 1, 0] - Root[4 + 2*#1 + #1^2 + #1^3 & , 2, 0])*Root[4 + 2*#1 + #1^2 + #1^3 & , 2, 0]*(4 + Root[4 + 2*#1 + #1^2 + #1^3 & , 2, 0]^2)*(Root[4 + 2*#1 + #1^2 + #1^3 & , 1, 0] - Root[4 + 2*#1 + #1^2 + #1^3 & , 3, 0])*(Root[4 + 2*#1 + #1^2 + #1^3 & , 2, 0] - Root[4 + 2*#1 + #1^2 + #1^3 & , 3, 0])*((1 - 2*I) + Root[4 + 2*#1 + #1^2 + #1^3 & , 2, 0] + Root[4 + 2*#1 + #1^2 + #1^3 & , 3, 0])*((1 + 2*I) + Root[4 + 2*#1 + #1^2 + #1^3 & , 2, 0] + Root[4 + 2*#1 + #1^2 + #1^3 & , 3, 0])*(-2 + Root[4 + 2*#1 + #1^2 + #1^3 & , 2, 0]^2 + 2*Root[4 + 2*#1 + #1^2 + #1^3 & , 1, 0]*Root[4 + 2*#1 + #1^2 + #1^3 & , 3, 0])*(4 + Root[4 + 2*#1 + #1^2 + #1^3 & , 3, 0]^2))}}
Maple raw input
dsolve(diff(diff(diff(y(x),x),x),x)+diff(diff(y(x),x),x)+2*diff(y(x),x)+4*y(x) = sin(2*x), y(x),'implicit')
Maple raw output
y(x) = (-207500*exp(-1/150*(3*249^(1/2)*(46+3*249^(1/2))^(2/3)-46*(46+3*249^(1/2))^(2/3)-25*(46+3*249^(1/2))^(1/3)+50)*x)*cos(23/75*(46+3*3^(1/2)*83^(1/2))^(1/3)*x*((3^(1/2)-9/46*83^(1/2))*(46+3*3^(1/2)*83^(1/2))^(1/3)-25/46*3^(1/2)))*((46+3*3^(1/2)*83^(1/2))^(1/3)+(-3/25*3^(1/2)*83^(1/2)+117/50)*(46+3*3^(1/2)*83^(1/2))^(2/3)+27/2+(-138/625*3^(1/2)*83^(1/2)+4357/1250)*(46+3*3^(1/2)*83^(1/2))^(4/3))*Int(3/4150*83^(1/2)*((25/9*3^(1/2)*(46+3*3^(1/2)*83^(1/2))^(1/3)-46/9*(3^(1/2)-9/46*83^(1/2))*(46+3*3^(1/2)*83^(1/2))^(2/3))*cos(23/75*(46+3*3^(1/2)*83^(1/2))^(1/3)*x*((3^(1/2)-9/46*83^(1/2))*(46+3*3^(1/2)*83^(1/2))^(1/3)-25/46*3^(1/2)))+((249^(1/2)-46/3)*(46+3*249^(1/2))^(2/3)-25/3*(46+3*249^(1/2))^(1/3))*sin(23/75*(46+3*3^(1/2)*83^(1/2))^(1/3)*x*((3^(1/2)-9/46*83^(1/2))*(46+3*3^(1/2)*83^(1/2))^(1/3)-25/46*3^(1/2))))*sin(2*x)*exp(1/150*(3*249^(1/2)*(46+3*249^(1/2))^(2/3)-46*(46+3*249^(1/2))^(2/3)-25*(46+3*249^(1/2))^(1/3)+50)*x),x)-207500*exp(-1/150*(3*249^(1/2)*(46+3*249^(1/2))^(2/3)-46*(46+3*249^(1/2))^(2/3)-25*(46+3*249^(1/2))^(1/3)+50)*x)*sin(23/75*(46+3*3^(1/2)*83^(1/2))^(1/3)*x*((3^(1/2)-9/46*83^(1/2))*(46+3*3^(1/2)*83^(1/2))^(1/3)-25/46*3^(1/2)))*((46+3*3^(1/2)*83^(1/2))^(1/3)+(-3/25*3^(1/2)*83^(1/2)+117/50)*(46+3*3^(1/2)*83^(1/2))^(2/3)+27/2+(-138/625*3^(1/2)*83^(1/2)+4357/1250)*(46+3*3^(1/2)*83^(1/2))^(4/3))*Int(1/498*83^(1/2)*sin(2*x)*exp(1/150*(3*249^(1/2)*(46+3*249^(1/2))^(2/3)-46*(46+3*249^(1/2))^(2/3)-25*(46+3*249^(1/2))^(1/3)+50)*x)*(((-9/25*249^(1/2)+138/25)*(46+3*249^(1/2))^(2/3)+3*(46+3*249^(1/2))^(1/3))*cos(23/75*(46+3*3^(1/2)*83^(1/2))^(1/3)*x*((3^(1/2)-9/46*83^(1/2))*(46+3*3^(1/2)*83^(1/2))^(1/3)-25/46*3^(1/2)))+sin(23/75*(46+3*3^(1/2)*83^(1/2))^(1/3)*x*((3^(1/2)-9/46*83^(1/2))*(46+3*3^(1/2)*83^(1/2))^(1/3)-25/46*3^(1/2)))*(3^(1/2)*(46+3*3^(1/2)*83^(1/2))^(1/3)-46/25*(3^(1/2)-9/46*83^(1/2))*(46+3*3^(1/2)*83^(1/2))^(2/3))),x)+(-3750*83^(1/2)*3^(1/2)*(cos(2*x)-1/6*sin(2*x))*(46+3*3^(1/2)*83^(1/2))^(1/3)+(6900*3^(1/2)*83^(1/2)*cos(2*x)-525*3^(1/2)*83^(1/2)*sin(2*x)-112050*cos(2*x)+18675*sin(2*x))*(46+3*3^(1/2)*83^(1/2))^(2/3)-4357*sin(2*x)*(3^(1/2)*83^(1/2)-68724/4357)*(46+3*3^(1/2)*83^(1/2))^(4/3))*exp(-1/75*x*(3*3^(1/2)*83^(1/2)*(46+3*3^(1/2)*83^(1/2))^(2/3)-3*249^(1/2)*(46+3*249^(1/2))^(2/3)-46*(46+3*3^(1/2)*83^(1/2))^(2/3)+46*(46+3*249^(1/2))^(2/3)-25*(46+3*3^(1/2)*83^(1/2))^(1/3)+25*(46+3*249^(1/2))^(1/3)))+207500*(_C2*exp(-1/150*(3*249^(1/2)*(46+3*249^(1/2))^(2/3)-46*(46+3*249^(1/2))^(2/3)-25*(46+3*249^(1/2))^(1/3)+50)*x)*cos(1/150*(46*3^(1/2)-9*83^(1/2))*x*(46+3*3^(1/2)*83^(1/2))^(2/3)-1/6*(46+3*3^(1/2)*83^(1/2))^(1/3)*3^(1/2)*x)+_C3*exp(-1/150*(3*249^(1/2)*(46+3*249^(1/2))^(2/3)-46*(46+3*249^(1/2))^(2/3)-25*(46+3*249^(1/2))^(1/3)+50)*x)*sin(1/150*(46*3^(1/2)-9*83^(1/2))*x*(46+3*3^(1/2)*83^(1/2))^(2/3)-1/6*(46+3*3^(1/2)*83^(1/2))^(1/3)*3^(1/2)*x)+_C1*exp(1/75*(3*249^(1/2)*(46+3*249^(1/2))^(2/3)-46*(46+3*249^(1/2))^(2/3)-25*(46+3*249^(1/2))^(1/3)-25)*x))*((46+3*3^(1/2)*83^(1/2))^(1/3)+(-3/25*3^(1/2)*83^(1/2)+117/50)*(46+3*3^(1/2)*83^(1/2))^(2/3)+27/2+(-138/625*3^(1/2)*83^(1/2)+4357/1250)*(46+3*3^(1/2)*83^(1/2))^(4/3)))/(207500*(46+3*3^(1/2)*83^(1/2))^(1/3)+(-24900*3^(1/2)*83^(1/2)+485550)*(46+3*3^(1/2)*83^(1/2))^(2/3)+2801250+(-45816*3^(1/2)*83^(1/2)+723262)*(46+3*3^(1/2)*83^(1/2))^(4/3))