40.12.2 problem 7

Internal problem ID [6750]
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 : 7
Date solved : Monday, January 27, 2025 at 02:27:27 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 30

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

\[ y = c_2 \,x^{2}+c_1 x +\frac {\ln \left (x \right )^{2}}{2}-\frac {\ln \left (x^{2}\right )}{2}+\frac {3 \ln \left (x \right )}{2}+\frac {1}{4} \]

✓ Solution by Mathematica

Time used: 0.034 (sec). Leaf size: 38

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

\[ y(x)\to \frac {1}{4} \left (-2 \log \left (x^2\right )+2 \log ^2(x)+6 \log (x)+1\right )+c_2 x^2+c_1 x \]