ODE
\[ y'''(x)-2 y''(x)+3 y'(x)+10 y(x)=0 \] ODE Classification
[[_3rd_order, _missing_x]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.00936375 (sec), leaf count = 87
\[\left \{\left \{y(x)\to c_1 e^{x \text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+3 \text {$\#$1}+10\& ,1\right ]}+c_2 e^{x \text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+3 \text {$\#$1}+10\& ,2\right ]}+c_3 e^{x \text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+3 \text {$\#$1}+10\& ,3\right ]}\right \}\right \}\]
Maple ✓
cpu = 0.026 (sec), leaf count = 170
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\rm e}^{-{\frac { \left ( \left ( 154+3\,\sqrt {2649} \right ) ^{{\frac {2}{3}}}-2\,\sqrt [3]{154+3\,\sqrt {2649}}-5 \right ) x}{3\,\sqrt [3]{154+3\,\sqrt {2649}}}}}}+{\it \_C2}\,{{\rm e}^{{\frac { \left ( \left ( 154+3\,\sqrt {2649} \right ) ^{{\frac {2}{3}}}+4\,\sqrt [3]{154+3\,\sqrt {2649}}-5 \right ) x}{6\,\sqrt [3]{154+3\,\sqrt {2649}}}}}}\sin \left ( {\frac {\sqrt {3} \left ( \left ( 154+3\,\sqrt {2649} \right ) ^{{\frac {2}{3}}}+5 \right ) x}{6\,\sqrt [3]{154+3\,\sqrt {2649}}}} \right ) +{\it \_C3}\,{{\rm e}^{{\frac { \left ( \left ( 154+3\,\sqrt {2649} \right ) ^{{\frac {2}{3}}}+4\,\sqrt [3]{154+3\,\sqrt {2649}}-5 \right ) x}{6\,\sqrt [3]{154+3\,\sqrt {2649}}}}}}\cos \left ( {\frac {\sqrt {3} \left ( \left ( 154+3\,\sqrt {2649} \right ) ^{{\frac {2}{3}}}+5 \right ) x}{6\,\sqrt [3]{154+3\,\sqrt {2649}}}} \right ) \right \} \] 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*2649^(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)