75.20.25 problem 664

Internal problem ID [17159]
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 15.5 Linear equations with variable coefficients. The Lagrange method. Exercises page 148
Problem number : 664
Date solved : Tuesday, January 28, 2025 at 09:54:46 AM
CAS classification : [[_2nd_order, _missing_y]]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 26

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

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

✓ Solution by Mathematica

Time used: 0.037 (sec). Leaf size: 29

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

\[ y(x)\to x \log ^2(x)-(-2+c_1) x+(-2+c_1) x \log (x)+c_2 \]