4.43.15 $y^{‴}(x)+y^{″}(x)+2y^{\prime }(x)+4y(x)=\sin (2x)$

ODE
$$y^{‴}(x)+y^{″}(x)+2y^{\prime }(x)+4y(x)=\sin (2x)$$ ODE Classification

[[_3rd_order, _linear, _nonhomogeneous]]

Book solution method
TO DO

Mathematica ✓
cpu = 0.291977 (sec), leaf count = 1185

$$\left\{\{y(x)\to e^{x\text{Root}[{\mathrm{\#}\text{1}}^3+{\mathrm{\#}\text{1}}^2+2\mathrm{\#}\text{1}+4\mathrm{\&},1]}{c}_1+e^{x\text{Root}[{\mathrm{\#}\text{1}}^3+{\mathrm{\#}\text{1}}^2+2\mathrm{\#}\text{1}+4\mathrm{\&},2]}{c}_2+e^{x\text{Root}[{\mathrm{\#}\text{1}}^3+{\mathrm{\#}\text{1}}^2+2\mathrm{\#}\text{1}+4\mathrm{\&},3]}{c}_3+\frac{8(\text{Root}[{\mathrm{\#}\text{1}}^3+{\mathrm{\#}\text{1}}^2+2\mathrm{\#}\text{1}+4\mathrm{\&},2]\text{Root}[{\mathrm{\#}\text{1}}^3+{\mathrm{\#}\text{1}}^2+2\mathrm{\#}\text{1}+4\mathrm{\&},3](-252+(-70+26\text{Root}[{\mathrm{\#}\text{1}}^3+{\mathrm{\#}\text{1}}^2+2\mathrm{\#}\text{1}+4\mathrm{\&},1]+\text{Root}{[{\mathrm{\#}\text{1}}^3+{\mathrm{\#}\text{1}}^2+2\mathrm{\#}\text{1}+4\mathrm{\&},1]}^2)\text{Root}[{\mathrm{\#}\text{1}}^3+{\mathrm{\#}\text{1}}^2+2\mathrm{\#}\text{1}+4\mathrm{\&},3])+2(166-(64+118\text{Root}[{\mathrm{\#}\text{1}}^3+{\mathrm{\#}\text{1}}^2+2\mathrm{\#}\text{1}+4\mathrm{\&},1]+3\text{Root}{[{\mathrm{\#}\text{1}}^3+{\mathrm{\#}\text{1}}^2+2\mathrm{\#}\text{1}+4\mathrm{\&},1]}^2)\text{Root}[{\mathrm{\#}\text{1}}^3+{\mathrm{\#}\text{1}}^2+2\mathrm{\#}\text{1}+4\mathrm{\&},3]+(-84-15\text{Root}[{\mathrm{\#}\text{1}}^3+{\mathrm{\#}\text{1}}^2+2\mathrm{\#}\text{1}+4\mathrm{\&},1]+5\text{Root}{[{\mathrm{\#}\text{1}}^3+{\mathrm{\#}\text{1}}^2+2\mathrm{\#}\text{1}+4\mathrm{\&},1]}^2)\text{Root}{[{\mathrm{\#}\text{1}}^3+{\mathrm{\#}\text{1}}^2+2\mathrm{\#}\text{1}+4\mathrm{\&},3]}^2)+2\text{Root}{[{\mathrm{\#}\text{1}}^3+{\mathrm{\#}\text{1}}^2+2\mathrm{\#}\text{1}+4\mathrm{\&},2]}^2(-26-3\text{Root}[{\mathrm{\#}\text{1}}^3+{\mathrm{\#}\text{1}}^2+2\mathrm{\#}\text{1}+4\mathrm{\&},3]+18\text{Root}{[{\mathrm{\#}\text{1}}^3+{\mathrm{\#}\text{1}}^2+2\mathrm{\#}\text{1}+4\mathrm{\&},3]}^2+\text{Root}[{\mathrm{\#}\text{1}}^3+{\mathrm{\#}\text{1}}^2+2\mathrm{\#}\text{1}+4\mathrm{\&},1](10+25\text{Root}[{\mathrm{\#}\text{1}}^3+{\mathrm{\#}\text{1}}^2+2\mathrm{\#}\text{1}+4\mathrm{\&},3]+8\text{Root}{[{\mathrm{\#}\text{1}}^3+{\mathrm{\#}\text{1}}^2+2\mathrm{\#}\text{1}+4\mathrm{\&},3]}^2)))\cos (2x)+(\text{Root}[{\mathrm{\#}\text{1}}^3+{\mathrm{\#}\text{1}}^2+2\mathrm{\#}\text{1}+4\mathrm{\&},2](128+24\text{Root}[{\mathrm{\#}\text{1}}^3+{\mathrm{\#}\text{1}}^2+2\mathrm{\#}\text{1}+4\mathrm{\&},3]-5(-24-50\text{Root}[{\mathrm{\#}\text{1}}^3+{\mathrm{\#}\text{1}}^2+2\mathrm{\#}\text{1}+4\mathrm{\&},1]+3\text{Root}{[{\mathrm{\#}\text{1}}^3+{\mathrm{\#}\text{1}}^2+2\mathrm{\#}\text{1}+4\mathrm{\&},1]}^2)\text{Root}{[{\mathrm{\#}\text{1}}^3+{\mathrm{\#}\text{1}}^2+2\mathrm{\#}\text{1}+4\mathrm{\&},3]}^2)+4(24+(116-30\text{Root}[{\mathrm{\#}\text{1}}^3+{\mathrm{\#}\text{1}}^2+2\mathrm{\#}\text{1}+4\mathrm{\&},1]+23\text{Root}{[{\mathrm{\#}\text{1}}^3+{\mathrm{\#}\text{1}}^2+2\mathrm{\#}\text{1}+4\mathrm{\&},1]}^2)\text{Root}[{\mathrm{\#}\text{1}}^3+{\mathrm{\#}\text{1}}^2+2\mathrm{\#}\text{1}+4\mathrm{\&},3]+(36+6\text{Root}[{\mathrm{\#}\text{1}}^3+{\mathrm{\#}\text{1}}^2+2\mathrm{\#}\text{1}+4\mathrm{\&},1]+11\text{Root}{[{\mathrm{\#}\text{1}}^3+{\mathrm{\#}\text{1}}^2+2\mathrm{\#}\text{1}+4\mathrm{\&},1]}^2)\text{Root}{[{\mathrm{\#}\text{1}}^3+{\mathrm{\#}\text{1}}^2+2\mathrm{\#}\text{1}+4\mathrm{\&},3]}^2)+\text{Root}{[{\mathrm{\#}\text{1}}^3+{\mathrm{\#}\text{1}}^2+2\mathrm{\#}\text{1}+4\mathrm{\&},2]}^2(\text{Root}[{\mathrm{\#}\text{1}}^3+{\mathrm{\#}\text{1}}^2+2\mathrm{\#}\text{1}+4\mathrm{\&},1](-88+96\text{Root}[{\mathrm{\#}\text{1}}^3+{\mathrm{\#}\text{1}}^2+2\mathrm{\#}\text{1}+4\mathrm{\&},3]+25\text{Root}{[{\mathrm{\#}\text{1}}^3+{\mathrm{\#}\text{1}}^2+2\mathrm{\#}\text{1}+4\mathrm{\&},3]}^2)+4(52+25\text{Root}[{\mathrm{\#}\text{1}}^3+{\mathrm{\#}\text{1}}^2+2\mathrm{\#}\text{1}+4\mathrm{\&},3]+51\text{Root}{[{\mathrm{\#}\text{1}}^3+{\mathrm{\#}\text{1}}^2+2\mathrm{\#}\text{1}+4\mathrm{\&},3]}^2)))\sin (2x)}{\text{Root}{[{\mathrm{\#}\text{1}}^3+{\mathrm{\#}\text{1}}^2+2\mathrm{\#}\text{1}+4\mathrm{\&},1]}^2(\text{Root}[{\mathrm{\#}\text{1}}^3+{\mathrm{\#}\text{1}}^2+2\mathrm{\#}\text{1}+4\mathrm{\&},1]-\text{Root}[{\mathrm{\#}\text{1}}^3+{\mathrm{\#}\text{1}}^2+2\mathrm{\#}\text{1}+4\mathrm{\&},2])\text{Root}[{\mathrm{\#}\text{1}}^3+{\mathrm{\#}\text{1}}^2+2\mathrm{\#}\text{1}+4\mathrm{\&},2](4+\text{Root}{[{\mathrm{\#}\text{1}}^3+{\mathrm{\#}\text{1}}^2+2\mathrm{\#}\text{1}+4\mathrm{\&},2]}^2)(\text{Root}[{\mathrm{\#}\text{1}}^3+{\mathrm{\#}\text{1}}^2+2\mathrm{\#}\text{1}+4\mathrm{\&},1]-\text{Root}[{\mathrm{\#}\text{1}}^3+{\mathrm{\#}\text{1}}^2+2\mathrm{\#}\text{1}+4\mathrm{\&},3])(\text{Root}[{\mathrm{\#}\text{1}}^3+{\mathrm{\#}\text{1}}^2+2\mathrm{\#}\text{1}+4\mathrm{\&},2]-\text{Root}[{\mathrm{\#}\text{1}}^3+{\mathrm{\#}\text{1}}^2+2\mathrm{\#}\text{1}+4\mathrm{\&},3])((1-2i)+\text{Root}[{\mathrm{\#}\text{1}}^3+{\mathrm{\#}\text{1}}^2+2\mathrm{\#}\text{1}+4\mathrm{\&},2]+\text{Root}[{\mathrm{\#}\text{1}}^3+{\mathrm{\#}\text{1}}^2+2\mathrm{\#}\text{1}+4\mathrm{\&},3])((1+2i)+\text{Root}[{\mathrm{\#}\text{1}}^3+{\mathrm{\#}\text{1}}^2+2\mathrm{\#}\text{1}+4\mathrm{\&},2]+\text{Root}[{\mathrm{\#}\text{1}}^3+{\mathrm{\#}\text{1}}^2+2\mathrm{\#}\text{1}+4\mathrm{\&},3])(-2+\text{Root}{[{\mathrm{\#}\text{1}}^3+{\mathrm{\#}\text{1}}^2+2\mathrm{\#}\text{1}+4\mathrm{\&},2]}^2+2\text{Root}[{\mathrm{\#}\text{1}}^3+{\mathrm{\#}\text{1}}^2+2\mathrm{\#}\text{1}+4\mathrm{\&},1]\text{Root}[{\mathrm{\#}\text{1}}^3+{\mathrm{\#}\text{1}}^2+2\mathrm{\#}\text{1}+4\mathrm{\&},3])(4+\text{Root}{[{\mathrm{\#}\text{1}}^3+{\mathrm{\#}\text{1}}^2+2\mathrm{\#}\text{1}+4\mathrm{\&},3]}^2)}\}\right\}$$

Maple ✓
cpu = 0.714 (sec), leaf count = 1277

$$\{y\left(x\right)=\frac{1}{207500\sqrt[3]{46+3\sqrt{3}\sqrt{83}}+(-24900\sqrt{3}\sqrt{83}+485550){(46+3\sqrt{3}\sqrt{83})}^{\frac{2}{3}}+2801250+(-45816\sqrt{3}\sqrt{83}+723262){(46+3\sqrt{3}\sqrt{83})}^{\frac{4}{3}}}(-207500{\mathrm{e}}^{-\frac{(3\sqrt{249}{(46+3\sqrt{249})}^{2/3}-46{(46+3\sqrt{249})}^{2/3}-25\sqrt[3]{46+3\sqrt{249}}+50)x}{150}}\cos \left(\frac{23\sqrt[3]{46+3\sqrt{3}\sqrt{83}}x((\sqrt{3}-\frac{9\sqrt{83}}{46})\sqrt[3]{46+3\sqrt{3}\sqrt{83}}-\frac{25\sqrt{3}}{46})}{75}\right)(\sqrt[3]{46+3\sqrt{3}\sqrt{83}}+(-\frac{3\sqrt{3}\sqrt{83}}{25}+\frac{117}{50}){(46+3\sqrt{3}\sqrt{83})}^{2/3}+\frac{27}{2}+(-\frac{138\sqrt{3}\sqrt{83}}{625}+\frac{4357}{1250}){(46+3\sqrt{3}\sqrt{83})}^{4/3})\int \frac{3\sqrt{83}\sin \left(2x\right)}{4150}((\frac{25\sqrt{3}\sqrt[3]{46+3\sqrt{3}\sqrt{83}}}{9}-\frac{(46\sqrt{3}-9\sqrt{83}){(46+3\sqrt{3}\sqrt{83})}^{2/3}}{9})\cos \left(\frac{23\sqrt[3]{46+3\sqrt{3}\sqrt{83}}x((\sqrt{3}-\frac{9\sqrt{83}}{46})\sqrt[3]{46+3\sqrt{3}\sqrt{83}}-\frac{25\sqrt{3}}{46})}{75}\right)+((\sqrt{249}-\frac{46}{3}){(46+3\sqrt{249})}^{2/3}-\frac{25\sqrt[3]{46+3\sqrt{249}}}{3})\sin \left(\frac{23\sqrt[3]{46+3\sqrt{3}\sqrt{83}}x((\sqrt{3}-\frac{9\sqrt{83}}{46})\sqrt[3]{46+3\sqrt{3}\sqrt{83}}-\frac{25\sqrt{3}}{46})}{75}\right)){\mathrm{e}}^{\frac{(3\sqrt{249}{(46+3\sqrt{249})}^{2/3}-46{(46+3\sqrt{249})}^{2/3}-25\sqrt[3]{46+3\sqrt{249}}+50)x}{150}}\mathrm{d}x-207500{\mathrm{e}}^{-\frac{(3\sqrt{249}{(46+3\sqrt{249})}^{2/3}-46{(46+3\sqrt{249})}^{2/3}-25\sqrt[3]{46+3\sqrt{249}}+50)x}{150}}\sin \left(\frac{23\sqrt[3]{46+3\sqrt{3}\sqrt{83}}x((\sqrt{3}-\frac{9\sqrt{83}}{46})\sqrt[3]{46+3\sqrt{3}\sqrt{83}}-\frac{25\sqrt{3}}{46})}{75}\right)(\sqrt[3]{46+3\sqrt{3}\sqrt{83}}+(-\frac{3\sqrt{3}\sqrt{83}}{25}+\frac{117}{50}){(46+3\sqrt{3}\sqrt{83})}^{2/3}+\frac{27}{2}+(-\frac{138\sqrt{3}\sqrt{83}}{625}+\frac{4357}{1250}){(46+3\sqrt{3}\sqrt{83})}^{4/3})\int \frac{\sqrt{83}\sin \left(2x\right)}{498}{\mathrm{e}}^{\frac{(3\sqrt{249}{(46+3\sqrt{249})}^{2/3}-46{(46+3\sqrt{249})}^{2/3}-25\sqrt[3]{46+3\sqrt{249}}+50)x}{150}}(((-\frac{9\sqrt{249}}{25}+\frac{138}{25}){(46+3\sqrt{249})}^{2/3}+3\sqrt[3]{46+3\sqrt{249}})\cos \left(\frac{23\sqrt[3]{46+3\sqrt{3}\sqrt{83}}x((\sqrt{3}-\frac{9\sqrt{83}}{46})\sqrt[3]{46+3\sqrt{3}\sqrt{83}}-\frac{25\sqrt{3}}{46})}{75}\right)+\sin \left(\frac{23\sqrt[3]{46+3\sqrt{3}\sqrt{83}}x((\sqrt{3}-\frac{9\sqrt{83}}{46})\sqrt[3]{46+3\sqrt{3}\sqrt{83}}-\frac{25\sqrt{3}}{46})}{75}\right)(\sqrt{3}\sqrt[3]{46+3\sqrt{3}\sqrt{83}}-\frac{(46\sqrt{3}-9\sqrt{83}){(46+3\sqrt{3}\sqrt{83})}^{2/3}}{25}))\mathrm{d}x+(-3750\sqrt{83}\sqrt{3}(\cos \left(2x\right)-1/6\sin \left(2x\right))\sqrt[3]{46+3\sqrt{3}\sqrt{83}}+(6900\sqrt{3}\sqrt{83}\cos \left(2x\right)-525\sqrt{3}\sqrt{83}\sin \left(2x\right)-112050\cos \left(2x\right)+18675\sin \left(2x\right)){(46+3\sqrt{3}\sqrt{83})}^{\frac{2}{3}}-4357\sin \left(2x\right)(\sqrt{3}\sqrt{83}-\frac{68724}{4357}){(46+3\sqrt{3}\sqrt{83})}^{4/3}){\mathrm{e}}^{-\frac{x(3\sqrt{3}\sqrt{83}{(46+3\sqrt{3}\sqrt{83})}^{2/3}-3\sqrt{249}{(46+3\sqrt{249})}^{2/3}-46{(46+3\sqrt{3}\sqrt{83})}^{2/3}+46{(46+3\sqrt{249})}^{2/3}-25\sqrt[3]{46+3\sqrt{3}\sqrt{83}}+25\sqrt[3]{46+3\sqrt{249}})}{75}}+207500(\mathit{\_}\mathit{C}\mathit{2}{\mathrm{e}}^{-\frac{(3\sqrt{249}{(46+3\sqrt{249})}^{2/3}-46{(46+3\sqrt{249})}^{2/3}-25\sqrt[3]{46+3\sqrt{249}}+50)x}{150}}\cos (\frac{(46\sqrt{3}-9\sqrt{83})x{(46+3\sqrt{3}\sqrt{83})}^{2/3}}{150}-1/6\sqrt[3]{46+3\sqrt{3}\sqrt{83}}\sqrt{3}x)+\mathit{\_}\mathit{C}\mathit{3}{\mathrm{e}}^{-\frac{(3\sqrt{249}{(46+3\sqrt{249})}^{2/3}-46{(46+3\sqrt{249})}^{2/3}-25\sqrt[3]{46+3\sqrt{249}}+50)x}{150}}\sin (\frac{(46\sqrt{3}-9\sqrt{83})x{(46+3\sqrt{3}\sqrt{83})}^{2/3}}{150}-1/6\sqrt[3]{46+3\sqrt{3}\sqrt{83}}\sqrt{3}x)+\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^{\frac{(3\sqrt{249}{(46+3\sqrt{249})}^{2/3}-46{(46+3\sqrt{249})}^{2/3}-25\sqrt[3]{46+3\sqrt{249}}-25)x}{75}})(\sqrt[3]{46+3\sqrt{3}\sqrt{83}}+(-\frac{3\sqrt{3}\sqrt{83}}{25}+\frac{117}{50}){(46+3\sqrt{3}\sqrt{83})}^{2/3}+\frac{27}{2}+(-\frac{138\sqrt{3}\sqrt{83}}{625}+\frac{4357}{1250}){(46+3\sqrt{3}\sqrt{83})}^{4/3}))\}$$ 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)-4
6*(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))*(4
6+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)+28012
50+(-45816*3^(1/2)*83^(1/2)+723262)*(46+3*3^(1/2)*83^(1/2))^(4/3))