Internal problem ID [7289]
Book: Own collection of miscellaneous problems
Section: section 4.0
Problem number: 65.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-\left (x^{2}+3\right ) y=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 30
dsolve(diff(y(x),x$2)=(x^2+3)*y(x),y(x), singsol=all)
\[ y \left (x \right ) = x \left (c_{2} \sqrt {\pi }\, \operatorname {erf}\left (x \right )+c_{1} \right ) {\mathrm e}^{\frac {x^{2}}{2}}+{\mathrm e}^{-\frac {x^{2}}{2}} c_{2} \]
✓ Solution by Mathematica
Time used: 0.125 (sec). Leaf size: 46
DSolve[y''[x]==(x^2+3)*y[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-\frac {x^2}{2}} \left (-\sqrt {\pi } c_2 e^{x^2} x \text {erf}(x)+c_1 e^{x^2} x-c_2\right ) \]