Internal problem ID [2176]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 20, page 90
Problem number: 3.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+4 y=x^{2}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 23
dsolve(diff(y(x),x$2)+4*y(x)=x^2,y(x), singsol=all)
\[ y = c_{2} \sin \left (2 x \right )+\cos \left (2 x \right ) c_{1} +\frac {x^{2}}{4}-\frac {1}{8} \]
✓ Solution by Mathematica
Time used: 0.012 (sec). Leaf size: 30
DSolve[y''[x]+4*y[x]==x^2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {x^2}{4}+c_1 \cos (2 x)+c_2 \sin (2 x)-\frac {1}{8} \]