83.26.10 problem 10

Internal problem ID [19334]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter VI. Homogeneous linear equations with variable coefficients. Exercise VI (C) at page 93
Problem number : 10
Date solved : Tuesday, January 28, 2025 at 01:34:28 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }+3 x y^{\prime }-3 y&=x \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 21

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

\[ y \left (x \right ) = \frac {c_{2}}{x^{3}}+c_{1} x -\frac {x}{16}+\frac {x \ln \left (x \right )}{4} \]

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 27

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

\[ y(x)\to \frac {c_1}{x^3}+\frac {1}{4} x \log (x)+\left (-\frac {1}{16}+c_2\right ) x \]