Internal problem ID [5261]
Book: An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY
1961
Section: Chapter 3. Linear equations with variable coefficients. Page 121
Problem number: 1(f).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-2 x y^{\prime }+2 y=0} \end {gather*} Given that one solution of the ode is \begin {align*} y_1 &= x \end {align*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 23
dsolve([diff(y(x),x$2)-2*x*diff(y(x),x)+2*y(x)=0,x],y(x), singsol=all)
\[ y \relax (x ) = c_{1} x +c_{2} \left (-\sqrt {\pi }\, \erfi \relax (x ) x +{\mathrm e}^{x^{2}}\right ) \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 31
DSolve[y''[x]-2*x*y'[x]+2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {\pi } c_2 x \text {Erfi}(x)+c_2 e^{x^2}+2 c_1 x \\ \end{align*}