15.15.14 problem 15

Internal problem ID [3218]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 24, page 109
Problem number : 15
Date solved : Monday, January 27, 2025 at 07:26:24 AM
CAS classification : [[_2nd_order, _missing_y]]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 33

dsolve(diff(y(x),x$2)-diff(y(x),x)=x*exp(2*x)*sin(x),y(x), singsol=all)
 

\[ y = \frac {\left (\left (-15 x +17\right ) \cos \left (x \right )+\sin \left (x \right ) \left (5 x +6\right )\right ) {\mathrm e}^{2 x}}{50}+{\mathrm e}^{x} c_{1} +c_2 \]

✓ Solution by Mathematica

Time used: 0.501 (sec). Leaf size: 46

DSolve[D[y[x],{x,2}]-D[y[x],x]==x*Exp[2*x]*Sin[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{50} e^{2 x} (5 x+6) \sin (x)-\frac {1}{50} e^{2 x} (15 x-17) \cos (x)+c_1 e^x+c_2 \]