Internal problem ID [13521]
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: 43.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} y^{\prime \prime }+3 x y^{\prime }+2 y=6} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 22
dsolve(x^2*diff(y(x),x$2)+3*x*diff(y(x),x)+2*y(x)=6,y(x), singsol=all)
\[ y \left (x \right ) = \frac {\sin \left (\ln \left (x \right )\right ) c_{2}}{x}+\frac {\cos \left (\ln \left (x \right )\right ) c_{1}}{x}+3 \]
✓ Solution by Mathematica
Time used: 0.025 (sec). Leaf size: 25
DSolve[x^2*y''[x]+3*x*y'[x]+2*y[x]==6,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {3 x+c_2 \cos (\log (x))+c_1 \sin (\log (x))}{x} \]