83.35.10 problem 10

Internal problem ID [19430]
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. Misc. Exercise on chapter VII. Page 118
Problem number : 10
Date solved : Tuesday, January 28, 2025 at 01:42:13 PM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} {\mathrm e}^{x} \left (x y^{\prime \prime }-y^{\prime }\right )&=x^{3} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 25

dsolve(exp(x^2/x)*(x*diff(y(x),x$2)-diff(y(x),x))=x^3,y(x), singsol=all)
 

\[ y \left (x \right ) = \left (x^{2}+3 x +3\right ) {\mathrm e}^{-x}+\frac {c_{1} x^{2}}{2}+c_{2} \]

✓ Solution by Mathematica

Time used: 0.171 (sec). Leaf size: 31

DSolve[Exp[x^2/x]*(x*D[y[x],{x,2}]-D[y[x],x])==x^3,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-x} \left (x^2+3 x+3\right )+\frac {c_1 x^2}{2}+c_2 \]