Internal problem ID [15429]
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 ODE’s). Section 15.5 Linear equations with variable coefficients.
The Lagrange method. Exercises page 148
Problem number: 664.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
\[ \boxed {x \ln \left (x \right ) y^{\prime \prime }-y^{\prime }=\ln \left (x \right )^{2}} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 26
dsolve(x*ln(x)*diff(y(x),x$2)-diff(y(x),x)=ln(x)^2,y(x), singsol=all)
\[ y \left (x \right ) = \ln \left (x \right )^{2} x +x \left (c_{1} -2\right ) \ln \left (x \right )+\left (-c_{1} +2\right ) x +c_{2} \]
✓ Solution by Mathematica
Time used: 0.049 (sec). Leaf size: 29
DSolve[x*Log[x]*y''[x]-y'[x]==Log[x]^2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to x \log ^2(x)-(-2+c_1) x+(-2+c_1) x \log (x)+c_2 \]