60.3.50 problem 1051

Internal problem ID [11060]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1051
Date solved : Monday, January 27, 2025 at 10:42:53 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-3\right ) y-{\mathrm e}^{x^{2}}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.006 (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)
 

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

✓ Solution by Mathematica

Time used: 0.040 (sec). Leaf size: 34

DSolve[-E^x^2 + (-3 + 4*x^2)*y[x] - 4*x*D[y[x],x] + D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{2} e^{(x-1) x} \left (-2 e^x+c_2 e^{2 x}+2 c_1\right ) \]