4.46 problem 1494

Internal problem ID [9073]

Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 3, linear third order
Problem number: 1494.
ODE order: 3.
ODE degree: 1.

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

Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime \prime }+5 y^{\prime \prime } x +4 y^{\prime }-\ln \relax (x )=0} \end {gather*}

Solution by Maple

Time used: 0.002 (sec). Leaf size: 25

dsolve(x^2*diff(diff(diff(y(x),x),x),x)+5*x*diff(diff(y(x),x),x)+4*diff(y(x),x)-ln(x)=0,y(x), singsol=all)
 

\[ y \relax (x ) = c_{1}+\frac {c_{2} \ln \relax (x )}{x}+\frac {c_{3}}{x}+\frac {x \left (\ln \relax (x )-2\right )}{4} \]

Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 43

DSolve[-Log[x] + 4*y'[x] + 5*x*y''[x] + x^2*Derivative[3][y][x] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {\left (x^2-8 c_2\right ) \log (x)-2 \left (x^2-2 c_3 x+2 c_1+4 c_2\right )}{4 x} \\ \end{align*}