83.49.12 problem Ex 12 page 128

Internal problem ID [19625]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Book Solved Excercises. Chapter VIII. Linear equations of second order
Problem number : Ex 12 page 128
Date solved : Tuesday, January 28, 2025 at 02:05:04 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 (2 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 23

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

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

✓ Solution by Mathematica

Time used: 0.071 (sec). Leaf size: 57

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

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