Internal problem ID [2246]
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: 14.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
\[ \boxed {y^{\prime \prime }+2 y^{\prime }=x^{3} \sin \left (2 x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 69
dsolve(diff(y(x),x$2)+2*diff(y(x),x)=x^3*sin(2*x),y(x), singsol=all)
\[ y = -\frac {\cos \left (2 x \right ) x^{3}}{8}+\frac {3 x^{2} \sin \left (2 x \right )}{8}-\frac {15 \sin \left (2 x \right )}{64}+\frac {15 \cos \left (2 x \right ) x}{32}+\frac {3 \sin \left (2 x \right ) x}{32}-\frac {x^{3} \sin \left (2 x \right )}{8}-\frac {3 \cos \left (2 x \right ) x^{2}}{16}-\frac {c_{1} {\mathrm e}^{-2 x}}{2}+c_{2} \]
✓ Solution by Mathematica
Time used: 0.435 (sec). Leaf size: 61
DSolve[y''[x]+2*y'[x]==x^3*Sin[2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {1}{32} x \left (4 x^2+6 x-15\right ) \cos (2 x)+\frac {1}{64} \left (-8 x^3+24 x^2+6 x-15\right ) \sin (2 x)-\frac {1}{2} c_1 e^{-2 x}+c_2 \]