75.19.12 problem 629

Internal problem ID [17128]
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 : 629
Date solved : Tuesday, January 28, 2025 at 09:53:44 AM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 25

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

\[ y = \frac {c_{1}}{x}+c_{2} x^{2}+\frac {\cos \left (\ln \left (x \right )\right )}{10}-\frac {3 \sin \left (\ln \left (x \right )\right )}{10} \]

✓ Solution by Mathematica

Time used: 0.039 (sec). Leaf size: 56

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

\[ y(x)\to \frac {x^3 \int _1^x\frac {\sin (\log (K[2]))}{3 K[2]^3}dK[2]+\int _1^x-\frac {1}{3} \sin (\log (K[1]))dK[1]+c_2 x^3+c_1}{x} \]