83.49.13 problem Ex 13 page 130

Internal problem ID [19626]
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 13 page 130
Date solved : Tuesday, January 28, 2025 at 02:05:09 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-\left (8 \,{\mathrm e}^{2 x}+2\right ) y^{\prime }+4 \,{\mathrm e}^{4 x} y&={\mathrm e}^{6 x} \end{align*}

✓ Solution by Maple

Time used: 0.095 (sec). Leaf size: 39

dsolve(diff(y(x),x$2)-(8*exp(2*x)+2)*diff(y(x),x)+4*exp(4*x)*y(x)=exp(6*x),y(x), singsol=all)
 

\[ y \left (x \right ) = {\mathrm e}^{{\mathrm e}^{2 x} \left (2+\sqrt {3}\right )} c_{2} +{\mathrm e}^{-{\mathrm e}^{2 x} \left (-2+\sqrt {3}\right )} c_{1} +\frac {{\mathrm e}^{2 x}}{4}+1 \]

✓ Solution by Mathematica

Time used: 0.283 (sec). Leaf size: 53

DSolve[D[y[x],{x,2}]-(8*Exp[2*x]+2)*D[y[x],x]+4*Exp[4*x]*y[x]==Exp[6*x],y[x],x,IncludeSingularSolutions -> True]
 

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