Internal problem ID [13471]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 24. Variation of parameters. Additional exercises page 444
Problem number: 24.2 (a).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _nonhomogeneous]]
\[ \boxed {x^{2} y^{\prime \prime }-2 y^{\prime } x -4 y=\frac {10}{x}} \] With initial conditions \begin {align*} [y \left (1\right ) = 3, y^{\prime }\left (1\right ) = -15] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 19
dsolve([x^2*diff(y(x),x$2)-2*x*diff(y(x),x)-4*y(x)=10/x,y(1) = 3, D(y)(1) = -15],y(x), singsol=all)
\[ y = \frac {-2 x^{5}-2 \ln \left (x \right )+5}{x} \]
✓ Solution by Mathematica
Time used: 0.022 (sec). Leaf size: 20
DSolve[{x^2*y''[x]-2*x*y'[x]-4*y[x]==10/x,{y[1]==3,y'[1]==-15}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {-2 x^5-2 \log (x)+5}{x} \]