60.3.11 problem 1011

Internal problem ID [11021]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1011
Date solved : Monday, January 27, 2025 at 10:42:01 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-\left (x^{2}+1\right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 17

dsolve(diff(diff(y(x),x),x)-(x^2+1)*y(x)=0,y(x), singsol=all)
 

\[ y = {\mathrm e}^{\frac {x^{2}}{2}} \left (c_{1} +\operatorname {erf}\left (x \right ) c_{2} \right ) \]

✓ Solution by Mathematica

Time used: 0.017 (sec). Leaf size: 33

DSolve[(-1 - x^2)*y[x] + D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_1 \operatorname {ParabolicCylinderD}\left (-1,\sqrt {2} x\right )+c_2 \operatorname {ParabolicCylinderD}\left (0,i \sqrt {2} x\right ) \]