75.19.13 problem 630

Internal problem ID [17129]
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 : 630
Date solved : Tuesday, January 28, 2025 at 09:53:47 AM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

\begin{align*} x^{2} y^{\prime \prime }-x y^{\prime }-3 y&=-\frac {16 \ln \left (x \right )}{x} \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 30

dsolve(x^2*diff(y(x),x$2)-x*diff(y(x),x)-3*y(x)=-16*ln(x)/x,y(x), singsol=all)
 

\[ y = \frac {4 c_{2} x^{4}+8 \ln \left (x \right )^{2}+4 \ln \left (x \right )+4 c_{1} +1}{4 x} \]

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 35

DSolve[x^2*D[y[x],{x,2}]-x*D[y[x],x]-3*y[x]==-16*Log[x]/x,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {4 c_2 x^4+8 \log ^2(x)+4 \log (x)+1+4 c_1}{4 x} \]