Internal problem ID [13454]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 22. Method of undetermined coefficients. Additional exercises page
412
Problem number: 22.15 (f).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _nonhomogeneous]]
\[ \boxed {2 x^{2} y^{\prime \prime }+5 y^{\prime } x +y=\frac {10}{x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 24
dsolve(2*x^2*diff(y(x),x$2)+5*x*diff(y(x),x)+y(x)=10/x,y(x), singsol=all)
\[ y = \frac {c_{1}}{x}+\frac {c_{2}}{\sqrt {x}}-\frac {10 \left (\ln \left (x \right )+2\right )}{x} \]
✓ Solution by Mathematica
Time used: 0.015 (sec). Leaf size: 25
DSolve[2*x^2*y''[x]+5*x*y'[x]+y[x]==10/x,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {-10 \log (x)+c_2 \sqrt {x}-20+c_1}{x} \]