Internal problem ID [12427]
Book: Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section: Chapter 4. N-th Order Linear Differential Equations. Exercises 4.1, page 186
Problem number: 4.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
\[ \boxed {x \left (x -3\right ) y^{\prime \prime }+3 y^{\prime }=x^{2}} \] With initial conditions \begin {align*} [y \left (5\right ) = 0, y^{\prime }\left (5\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 24
dsolve([x*(x-3)*diff(y(x),x$2)+3*diff(y(x),x)=x^2,y(5) = 0, D(y)(5) = 1],y(x), singsol=all)
\[ y \left (x \right ) = \frac {x^{2}}{2}-\frac {8 x}{5}-\frac {24 \ln \left (x -3\right )}{5}-\frac {9}{2}+\frac {24 \ln \left (2\right )}{5} \]
✓ Solution by Mathematica
Time used: 0.069 (sec). Leaf size: 29
DSolve[{x*(x-3)*y''[x]+3*y'[x]==x^2,{y[5]==0,y'[5]==1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{10} \left (5 x^2-16 x-48 \log (x-3)-45+48 \log (2)\right ) \]