35.7.17 problem 20

Internal problem ID [6199]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 7. Other second-Order equations. page 435
Problem number : 20
Date solved : Monday, January 27, 2025 at 01:47:32 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y&=6 x^{2} \ln \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 18

dsolve(x^2*diff(y(x),x$2)-3*x*diff(y(x),x)+4*y(x)=6*x^2*ln(x),y(x), singsol=all)
 

\[ y = x^{2} \left (c_{2} +c_{1} \ln \left (x \right )+\ln \left (x \right )^{3}\right ) \]

✓ Solution by Mathematica

Time used: 0.025 (sec). Leaf size: 22

DSolve[x^2*D[y[x],{x,2}]-3*x*D[y[x],x]+4*y[x]==6*x^2*Log[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x^2 \left (\log ^3(x)+2 c_2 \log (x)+c_1\right ) \]