73.17.40 problem 40

Internal problem ID [15574]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 25. Review exercises for part III. page 447
Problem number : 40
Date solved : Tuesday, January 28, 2025 at 08:02:30 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 2 x^{2} y^{\prime \prime }-x y^{\prime }-2 y&=10 x^{2} \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 26

dsolve(2*x^2*diff(y(x),x$2)-x*diff(y(x),x)-2*y(x)=10*x^2,y(x), singsol=all)
 

\[ y = c_{2} x^{2}+\frac {c_{1}}{\sqrt {x}}+\frac {2 x^{2} \left (-2+5 \ln \left (x \right )\right )}{5} \]

✓ Solution by Mathematica

Time used: 0.020 (sec). Leaf size: 31

DSolve[2*x^2*D[y[x],{x,2}]-x*D[y[x],x]-2*y[x]==10*x^2,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to 2 x^2 \log (x)+\left (-\frac {4}{5}+c_2\right ) x^2+\frac {c_1}{\sqrt {x}} \]