Internal problem ID [2213]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+y={\mathrm e}^{3 x} \left (1+\sin \left (2 x \right )\right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 33
dsolve(diff(y(x),x$2)+y(x)=exp(3*x)*(1+sin(2*x)),y(x), singsol=all)
\[ y = \sin \left (x \right ) c_{2} +\cos \left (x \right ) c_{1} -\frac {{\mathrm e}^{3 x} \left (-\sin \left (2 x \right )-3+2 \cos \left (2 x \right )\right )}{30} \]
✓ Solution by Mathematica
Time used: 0.288 (sec). Leaf size: 50
DSolve[y''[x]+y[x]==Exp[3*x]*(1+Sin[2*x]),y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{30} \left (3 e^{3 x}+e^{3 x} \sin (2 x)-2 e^{3 x} \cos (2 x)+30 c_1 \cos (x)+30 c_2 \sin (x)\right ) \]