10.10.17 problem 17

Internal problem ID [1349]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Chapter 3, Second order linear equations, section 3.6, Variation of Parameters. page 190
Problem number : 17
Date solved : Monday, January 27, 2025 at 04:51:58 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y&=x^{2} \ln \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 20

dsolve(x^2*diff(y(x),x$2)-3*x*diff(y(x),x)+4*y(x) = x^2*ln(x),y(x), singsol=all)
 

\[ y = x^{2} \left (c_2 +\ln \left (x \right ) c_1 +\frac {\ln \left (x \right )^{3}}{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.028 (sec). Leaf size: 27

DSolve[x^2*D[y[x],{x,2}]-3*x*D[y[x],x]+4*y[x] == x^2*Log[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{6} x^2 \left (\log ^3(x)+12 c_2 \log (x)+6 c_1\right ) \]