Internal problem ID [2245]
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: 13.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-y=x \sin \left (2 x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 28
dsolve(diff(y(x),x$2)-y(x)=x*sin(2*x),y(x), singsol=all)
\[ y = {\mathrm e}^{-x} c_{2} +c_{1} {\mathrm e}^{x}-\frac {4 \cos \left (2 x \right )}{25}-\frac {\sin \left (2 x \right ) x}{5} \]
✓ Solution by Mathematica
Time used: 0.019 (sec). Leaf size: 37
DSolve[y''[x]-y[x]==x*Sin[2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {1}{5} x \sin (2 x)-\frac {4}{25} \cos (2 x)+c_1 e^x+c_2 e^{-x} \]