Internal problem ID [12426]
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: 3.
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 (1\right ) = 0, y^{\prime }\left (1\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 11
dsolve([x*(x-3)*diff(y(x),x$2)+3*diff(y(x),x)=x^2,y(1) = 0, D(y)(1) = 1],y(x), singsol=all)
\[ y \left (x \right ) = -\frac {1}{2}+\frac {x^{2}}{2} \]
✓ Solution by Mathematica
Time used: 0.08 (sec). Leaf size: 14
DSolve[{x*(x-3)*y''[x]+3*y'[x]==x^2,{y[1]==0,y'[1]==1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} \left (x^2-1\right ) \]