40.12.1 problem 6

Internal problem ID [6749]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 17. Linear equations with variable coefficients (Cauchy and Legndre). Supplemetary problems. Page 110
Problem number : 6
Date solved : Monday, January 27, 2025 at 02:27:24 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 27

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

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

✓ Solution by Mathematica

Time used: 0.038 (sec). Leaf size: 30

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

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