15.14.12 problem 12

Internal problem ID [3184]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 23, page 106
Problem number : 12
Date solved : Monday, January 27, 2025 at 07:25:20 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 33

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

\[ y = \frac {\left (2 \cos \left (x \right ) \sin \left (x \right )+5-4 \cos \left (x \right )^{2}\right ) {\mathrm e}^{3 x}}{30}+\cos \left (x \right ) c_{1} +c_2 \sin \left (x \right ) \]

✓ Solution by Mathematica

Time used: 0.287 (sec). Leaf size: 50

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

\[ y(x)\to \frac {1}{30} \left (3 e^{3 x}+e^{3 x} \sin (2 x)-2 e^{3 x} \cos (2 x)+30 c_1 \cos (x)+30 c_2 \sin (x)\right ) \]