83.26.6 problem 6

Internal problem ID [19330]
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 : 6
Date solved : Tuesday, January 28, 2025 at 01:34:19 PM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 27

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

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

✓ Solution by Mathematica

Time used: 0.025 (sec). Leaf size: 27

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

\[ y(x)\to \frac {x^m}{m^2-1}+c_2 x+\frac {c_1}{x} \]