8.11.39 problem 62

Internal problem ID [907]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 5.5, Nonhomogeneous equations and undetermined coefficients Page 351
Problem number : 62
Date solved : Monday, January 27, 2025 at 03:17:55 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y&=x^{2}-1 \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 38

dsolve((x^2-1)*diff(y(x),x$2)-2*x*diff(y(x),x)+2*y(x)=x^2-1,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.012 (sec). Leaf size: 22

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

\[ y(x)\to x^2 (x \log (x)+(-1+c_2) x+c_1) \]