Internal problem ID [9384]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1051.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-4 y^{\prime } x +\left (4 x^{2}-3\right ) y={\mathrm e}^{x^{2}}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 27
dsolve(diff(diff(y(x),x),x)-4*x*diff(y(x),x)+(4*x^2-3)*y(x)-exp(x^2)=0,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: 0.042 (sec). Leaf size: 34
DSolve[-E^x^2 + (-3 + 4*x^2)*y[x] - 4*x*y'[x] + y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} e^{(x-1) x} \left (-2 e^x+c_2 e^{2 x}+2 c_1\right ) \]