Internal problem ID [2208]
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: 7.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+3 y^{\prime }-2 y=\sin \left (2 x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 39
dsolve(diff(y(x),x$2)+3*diff(y(x),x)-2*y(x)=sin(2*x),y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{\frac {\left (-3+\sqrt {17}\right ) x}{2}} c_{2} +{\mathrm e}^{-\frac {\left (3+\sqrt {17}\right ) x}{2}} c_{1} -\frac {\sin \left (2 x \right )}{12}-\frac {\cos \left (2 x \right )}{12} \]
✓ Solution by Mathematica
Time used: 0.346 (sec). Leaf size: 52
DSolve[y''[x]+3*y'[x]-2*y[x]==Sin[2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {1}{12} \cos (2 x)+e^{-\frac {1}{2} \left (3+\sqrt {17}\right ) x} \left (c_2 e^{\sqrt {17} x}+c_1\right )-\frac {1}{6} \sin (x) \cos (x) \]