Internal problem ID [7972]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 496.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+\left (-3+x \right ) y^{\prime }+3 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 68
dsolve(diff(y(x),x$2)+(x-3)*diff(y(x),x)+3*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} {\mathrm e}^{-\frac {1}{2} x^{2}+3 x} \left (x^{2}-6 x +8\right )+c_{2} {\mathrm e}^{-\frac {1}{2} x^{2}+3 x} \left (x^{2}-6 x +8\right ) \left (\int \frac {{\mathrm e}^{\frac {1}{2} x^{2}-3 x}}{\left (x -2\right )^{2} \left (x -4\right )^{2}}d x \right ) \]
✓ Solution by Mathematica
Time used: 0.275 (sec). Leaf size: 90
DSolve[y''[x]+(x-3)*y'[x]+3*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{4} e^{-\frac {1}{2} (x-6) x-8} \left (e^{7/2} \sqrt {2 \pi } c_2 \left (x^2-6 x+8\right ) \text {erfi}\left (\frac {x-3}{\sqrt {2}}\right )+4 e^8 c_1 \left (x^2-6 x+8\right )-2 c_2 e^{\frac {1}{2} (x-4)^2+x} (x-3)\right ) \]