82.39.14 problem Ex. 14

Internal problem ID [18946]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter VII. Linear equations with variable coefficients. End of chapter problems at page 91
Problem number : Ex. 14
Date solved : Tuesday, January 28, 2025 at 12:37:58 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} x^{2} y^{\prime \prime }-3 x y^{\prime }+y&=\frac {\ln \left (x \right ) \sin \left (\ln \left (x \right )\right )+1}{x} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 55

dsolve(x^2*diff(y(x),x$2)-3*x*diff(y(x),x)+y(x)=(ln(x)*sin(ln(x))+1)/x,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {22326 x^{3} x^{-\sqrt {3}} c_{1} +22326 x^{3} x^{\sqrt {3}} c_{2} +\left (1146+162 i+\left (1098+915 i\right ) \ln \left (x \right )\right ) x^{-i}+3721+\left (1146-162 i+\left (1098-915 i\right ) \ln \left (x \right )\right ) x^{i}}{22326 x} \]

✓ Solution by Mathematica

Time used: 0.482 (sec). Leaf size: 67

DSolve[x^2*D[y[x],{x,2}]-3*x*D[y[x],x]+y[x]==(Log[x]*Sin[Log[x]]+1)/x,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {3721 \left (6 c_2 x^{3+\sqrt {3}}+6 c_1 x^{3-\sqrt {3}}+1\right )+6 (305 \log (x)+54) \sin (\log (x))+12 (183 \log (x)+191) \cos (\log (x))}{22326 x} \]