75.19.15 problem 632

Internal problem ID [17131]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Chapter 2 (Higher order ODEs). Section 15.4 Nonhomogeneous linear equations with constant coefficients. The Euler equations. Exercises page 143
Problem number : 632
Date solved : Tuesday, January 28, 2025 at 09:53:51 AM
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)
 

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

✓ Solution by Mathematica

Time used: 0.024 (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]
 

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