Internal problem ID [7473]
Book: Second order enumerated odes
Section: section 2
Problem number: 32.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-3\right ) y={\mathrm e}^{x^{2}}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 27
dsolve(diff(y(x),x$2)-4*x*diff(y(x),x)+(4*x^2-3)*y(x)=exp(x^2),y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{x \left (x +1\right )} c_{2} +{\mathrm e}^{x \left (x -1\right )} c_{1} -{\mathrm e}^{x^{2}} \]
✓ Solution by Mathematica
Time used: 0.041 (sec). Leaf size: 34
DSolve[y''[x]-4*x*y'[x]+(4*x^2-3)*y[x]==Exp[x^2],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} e^{(x-1) x} \left (-2 e^x+c_2 e^{2 x}+2 c_1\right ) \]