4.43.24 $y^{‴}(x)-2y^{″}(x)+3y^{\prime }(x)+10y(x)=0$

ODE
$$y^{‴}(x)-2y^{″}(x)+3y^{\prime }(x)+10y(x)=0$$ ODE Classification

[[_3rd_order, _missing_x]]

Book solution method
TO DO

Mathematica ✓
cpu = 0.00936375 (sec), leaf count = 87

$$\left\{\{y(x)\to c_1{e}^{x\text{Root}[{\mathrm{\#}\text{1}}^3-2{\mathrm{\#}\text{1}}^2+3\mathrm{\#}\text{1}+10\mathrm{\&},1]}+c_2{e}^{x\text{Root}[{\mathrm{\#}\text{1}}^3-2{\mathrm{\#}\text{1}}^2+3\mathrm{\#}\text{1}+10\mathrm{\&},2]}+c_3{e}^{x\text{Root}[{\mathrm{\#}\text{1}}^3-2{\mathrm{\#}\text{1}}^2+3\mathrm{\#}\text{1}+10\mathrm{\&},3]}\}\right\}$$

Maple ✓
cpu = 0.026 (sec), leaf count = 170

$$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^{-\frac{({(154+3\sqrt{2649})}^{\frac{2}{3}}-2\sqrt[3]{154+3\sqrt{2649}}-5)x}{3\sqrt[3]{154+3\sqrt{2649}}}}+\mathit{\_}\mathit{C}\mathit{2}{\mathrm{e}}^{\frac{({(154+3\sqrt{2649})}^{\frac{2}{3}}+4\sqrt[3]{154+3\sqrt{2649}}-5)x}{6\sqrt[3]{154+3\sqrt{2649}}}}\sin \left(\frac{\sqrt{3}({(154+3\sqrt{2649})}^{\frac{2}{3}}+5)x}{6\sqrt[3]{154+3\sqrt{2649}}}\right)+\mathit{\_}\mathit{C}\mathit{3}{\mathrm{e}}^{\frac{({(154+3\sqrt{2649})}^{\frac{2}{3}}+4\sqrt[3]{154+3\sqrt{2649}}-5)x}{6\sqrt[3]{154+3\sqrt{2649}}}}\cos \left(\frac{\sqrt{3}({(154+3\sqrt{2649})}^{\frac{2}{3}}+5)x}{6\sqrt[3]{154+3\sqrt{2649}}}\right)\}$$ Mathematica raw input

DSolve[10*y[x] + 3*y'[x] - 2*y''[x] + y'''[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> E^(x*Root[10 + 3*#1 - 2*#1^2 + #1^3 & , 1, 0])*C[1] + E^(x*Root[10 + 3
*#1 - 2*#1^2 + #1^3 & , 2, 0])*C[2] + E^(x*Root[10 + 3*#1 - 2*#1^2 + #1^3 & , 3,
 0])*C[3]}}

Maple raw input

dsolve(diff(diff(diff(y(x),x),x),x)-2*diff(diff(y(x),x),x)+3*diff(y(x),x)+10*y(x) = 0, y(x),'implicit')

Maple raw output

y(x) = _C1*exp(-1/3*((154+3*2649^(1/2))^(2/3)-2*(154+3*2649^(1/2))^(1/3)-5)/(154
+3*2649^(1/2))^(1/3)*x)+_C2*exp(1/6/(154+3*2649^(1/2))^(1/3)*((154+3*2649^(1/2))
^(2/3)+4*(154+3*2649^(1/2))^(1/3)-5)*x)*sin(1/6/(154+3*2649^(1/2))^(1/3)*3^(1/2)
*((154+3*2649^(1/2))^(2/3)+5)*x)+_C3*exp(1/6/(154+3*2649^(1/2))^(1/3)*((154+3*26
49^(1/2))^(2/3)+4*(154+3*2649^(1/2))^(1/3)-5)*x)*cos(1/6/(154+3*2649^(1/2))^(1/3
)*3^(1/2)*((154+3*2649^(1/2))^(2/3)+5)*x)