Internal problem ID [13518]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {2 x^{2} y^{\prime \prime }-x y^{\prime }-2 y=10 x^{2}} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (x \right ) = c_{2} x^{2}+\frac {c_{1}}{\sqrt {x}}+\frac {2 x^{2} \left (-2+5 \ln \left (x \right )\right )}{5} \]
✓ Solution by Mathematica
Time used: 0.017 (sec). Leaf size: 31
DSolve[2*x^2*y''[x]-x*y'[x]-2*y[x]==10*x^2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to 2 x^2 \log (x)+\left (-\frac {4}{5}+c_2\right ) x^2+\frac {c_1}{\sqrt {x}} \]