Internal problem ID [2247]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
\[ \boxed {y^{\prime \prime }-y^{\prime }=x \,{\mathrm e}^{2 x} \sin \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 44
dsolve(diff(y(x),x$2)-diff(y(x),x)=x*exp(2*x)*sin(x),y(x), singsol=all)
\[ y = -\frac {3 \,{\mathrm e}^{2 x} \cos \left (x \right ) x}{10}+\frac {17 \,{\mathrm e}^{2 x} \cos \left (x \right )}{50}+\frac {{\mathrm e}^{2 x} \sin \left (x \right ) x}{10}+\frac {3 \,{\mathrm e}^{2 x} \sin \left (x \right )}{25}+c_{1} {\mathrm e}^{x}+c_{2} \]
✓ Solution by Mathematica
Time used: 0.486 (sec). Leaf size: 46
DSolve[y''[x]-y'[x]==x*Exp[2*x]*Sin[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{50} e^{2 x} (5 x+6) \sin (x)-\frac {1}{50} e^{2 x} (15 x-17) \cos (x)+c_1 e^x+c_2 \]