75.19.2 problem 619

Internal problem ID [17118]
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 : 619
Date solved : Tuesday, January 28, 2025 at 09:53:30 AM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

\begin{align*} x^{2} y^{\prime \prime }+3 x y^{\prime }+y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 14

dsolve(x^2*diff(y(x),x$2)+3*x*diff(y(x),x)+y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.025 (sec). Leaf size: 17

DSolve[x^2*D[y[x],{x,2}]+3*x*D[y[x],x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {c_2 \log (x)+c_1}{x} \]