Internal problem ID [5400]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 16. Linear equations with constant coefficients (Short methods). Supplemetary
problems. Page 107
Problem number: 34.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-y=x^{2}} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 21
dsolve(diff(y(x),x$2)-y(x)=x^2,y(x), singsol=all)
\[ y \left (x \right ) = c_{2} {\mathrm e}^{-x}+{\mathrm e}^{x} c_{1} -x^{2}-2 \]
✓ Solution by Mathematica
Time used: 0.013 (sec). Leaf size: 26
DSolve[y''[x]-y[x]==x^2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -x^2+c_1 e^x+c_2 e^{-x}-2 \]