83.30.1 problem 1

Internal problem ID [19380]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter VII. Exact differential equations and certain particular forms of equations. Exercise VII (D) at page 109
Problem number : 1
Date solved : Tuesday, January 28, 2025 at 01:36:20 PM
CAS classification : [[_2nd_order, _missing_y]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 15

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

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

✓ Solution by Mathematica

Time used: 0.011 (sec). Leaf size: 28

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

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