58.2.30 problem 30

Internal problem ID [9153]
Book : Second order enumerated odes
Section : section 2
Problem number : 30
Date solved : Monday, January 27, 2025 at 05:49:58 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-1\right ) y&=-3 \,{\mathrm e}^{x^{2}} \sin \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.019 (sec). Leaf size: 29

dsolve(diff(y(x),x$2)-4*x*diff(y(x),x)+(4*x^2-1)*y(x)=-3*exp(x^2)*sin(x),y(x), singsol=all)
 

\[ y = \frac {\left (\left (2 c_{2} +3 x \right ) \cos \left (x \right )+\sin \left (x \right ) \left (2 c_{1} -3\right )\right ) {\mathrm e}^{x^{2}}}{2} \]

✓ Solution by Mathematica

Time used: 0.090 (sec). Leaf size: 50

DSolve[D[y[x],{x,2}]-4*x*D[y[x],x]+(4*x^2-1)*y[x]==-3*Exp[x^2]*Sin[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{8} e^{x (x-i)} \left (6 x+e^{2 i x} (6 x+3 i-4 i c_2)-3 i+8 c_1\right ) \]