4.19 problem 1467

Internal problem ID [9046]

Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 3, linear third order
Problem number: 1467.
ODE order: 3.
ODE degree: 1.

CAS Maple gives this as type [[_3rd_order, _missing_x]]

Solve \begin {gather*} \boxed {y^{\prime \prime \prime }+\mathit {a2} y^{\prime \prime }+\mathit {a1} y^{\prime }+\mathit {a0} y=0} \end {gather*}

Solution by Maple

Time used: 0.001 (sec). Leaf size: 644

dsolve(diff(diff(diff(y(x),x),x),x)+a2*diff(diff(y(x),x),x)+a1*diff(y(x),x)+a0*y(x)=0,y(x), singsol=all)
 

\[ \text {Expression too large to display} \]

Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 84

DSolve[a0*y[x] + a1*y'[x] + a2*y''[x] + Derivative[3][y][x] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to c_1 e^{x \text {Root}\left [\text {$\#$1}^3+\text {$\#$1}^2 \text {a2}+\text {$\#$1} \text {a1}+\text {a0}\&,1\right ]}+c_2 e^{x \text {Root}\left [\text {$\#$1}^3+\text {$\#$1}^2 \text {a2}+\text {$\#$1} \text {a1}+\text {a0}\&,2\right ]}+c_3 e^{x \text {Root}\left [\text {$\#$1}^3+\text {$\#$1}^2 \text {a2}+\text {$\#$1} \text {a1}+\text {a0}\&,3\right ]} \\ \end{align*}