83.36.6 problem 6

Internal problem ID [19440]
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 : 6
Date solved : Tuesday, January 28, 2025 at 01:42:59 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 37

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

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

✓ Solution by Mathematica

Time used: 0.069 (sec). Leaf size: 48

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

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