83.36.7 problem 7

Internal problem ID [19441]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter VIII. Linear equations of second order. Excercise VIII (A) at page 125
Problem number : 7
Date solved : Tuesday, January 28, 2025 at 08:32:46 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime \prime }-x y^{\prime \prime }-y^{\prime }+y x&=0 \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 48

dsolve(diff(y(x),x$3)-x*diff(y(x),x$2)-diff(y(x),x)+x*y(x)=0,y(x), singsol=all)
 

\[ y \left (x \right ) = \operatorname {erf}\left (\frac {i \sqrt {2}\, \left (x -1\right )}{2}\right ) {\mathrm e}^{x -\frac {1}{2}} c_3 -\operatorname {erf}\left (\frac {i \sqrt {2}\, \left (x +1\right )}{2}\right ) {\mathrm e}^{-x -\frac {1}{2}} c_3 +c_{2} {\mathrm e}^{-x}+{\mathrm e}^{x} c_{1} \]

✓ Solution by Mathematica

Time used: 0.074 (sec). Leaf size: 70

DSolve[D[y[x],{x,3}]-x*D[y[x],{x,2}]-D[y[x],x]+x*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{2} e^{-x} \left (\sqrt {\frac {2 \pi }{e}} c_3 \left (e^{2 x} \text {erfi}\left (\frac {x-1}{\sqrt {2}}\right )-\text {erfi}\left (\frac {x+1}{\sqrt {2}}\right )\right )+2 c_2 e^{2 x}+2 c_1\right ) \]