8.11.35 problem 58

Internal problem ID [903]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 5.5, Nonhomogeneous equations and undetermined coefficients Page 351
Problem number : 58
Date solved : Wednesday, February 05, 2025 at 04:44:00 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y&=x^{3} \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 19

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

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

✓ 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]
 

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