83.26.18 problem 18

Internal problem ID [19342]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter VI. Homogeneous linear equations with variable coefficients. Exercise VI (C) at page 93
Problem number : 18
Date solved : Tuesday, January 28, 2025 at 01:34:48 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} x^{2} y^{\prime \prime }-3 x y^{\prime }+5 y&=x^{2} \sin \left (\ln \left (x \right )\right ) \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 29

dsolve(x^2*diff(y(x),x$2)-3*x*diff(y(x),x)+5*y(x)=x^2*sin(ln(x)),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.051 (sec). Leaf size: 32

DSolve[x^2*D[y[x],{x,2}]-3*x*D[y[x],x]+5*y[x]==x^2*Sin[Log[x]],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{2} x^2 (2 c_1 \sin (\log (x))-(\log (x)-2 c_2) \cos (\log (x))) \]