83.47.15 problem Ex 15 page 92

Internal problem ID [19592]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Book Solved Excercises. Chapter VI. Homogeneous linear equations with variable coefficients
Problem number : Ex 15 page 92
Date solved : Tuesday, January 28, 2025 at 02:00:30 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: 0.004 (sec). Leaf size: 53

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

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

✓ Solution by Mathematica

Time used: 0.407 (sec). Leaf size: 67

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

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