75.19.11 problem 628

Internal problem ID [17127]
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 : 628
Date solved : Tuesday, January 28, 2025 at 09:53:40 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+y&=x \left (6-\ln \left (x \right )\right ) \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 22

dsolve(x^2*diff(y(x),x$2)+x*diff(y(x),x)+y(x)=x*(6-ln(x)),y(x), singsol=all)
 

\[ y = \sin \left (\ln \left (x \right )\right ) c_{2} +\cos \left (\ln \left (x \right )\right ) c_{1} -\frac {x \left (\ln \left (x \right )-7\right )}{2} \]

✓ Solution by Mathematica

Time used: 0.172 (sec). Leaf size: 61

DSolve[x^2*D[y[x],{x,2}]+x*D[y[x],x]+y[x]==x*(6-Log[x]),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \cos (\log (x)) \int _1^x(\log (K[1])-6) \sin (\log (K[1]))dK[1]+\sin (\log (x)) \int _1^x-\cos (\log (K[2])) (\log (K[2])-6)dK[2]+c_1 \cos (\log (x))+c_2 \sin (\log (x)) \]