58.2.19 problem 20

Internal problem ID [9142]
Book : Second order enumerated odes
Section : section 2
Problem number : 20
Date solved : Monday, January 27, 2025 at 05:48:54 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 28

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

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

✓ Solution by Mathematica

Time used: 0.020 (sec). Leaf size: 27

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

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