Internal problem ID [15436]
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: 671.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {2 x^{2} \left (2-\ln \left (x \right )\right ) y^{\prime \prime }+x \left (4-\ln \left (x \right )\right ) y^{\prime }-y=\frac {\left (2-\ln \left (x \right )\right )^{2}}{\sqrt {x}}} \] With initial conditions \begin {align*} [y \left (\infty \right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 21
dsolve([2*x^2*(2-ln(x))*diff(y(x),x$2)+x*(4-ln(x))*diff(y(x),x)-y(x)=(2-ln(x))^2/sqrt(x),y(infinity) = 0],y(x), singsol=all)
\[ y \left (x \right ) = \frac {\sqrt {x}\, \ln \left (x \right ) c_{2} -\ln \left (x \right )+1}{\sqrt {x}} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[{2*x^2*(2-Log[x])*y''[x]+x*(4-Log[x])*y'[x]-y[x]==(2-Log[x])^2/Sqrt[x],{y[Infinity]==0}},y[x],x,IncludeSingularSolutions -> True]
Not solved