Internal problem ID [10245]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter VII, Linear differential equations with constant coefficients. Article 50. Method of
undetermined coefficients. Page 107
Problem number: Ex 1.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+4 y-x^{2}-\cos \left (x \right )=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 27
dsolve(diff(y(x),x$2)+4*y(x)=x^2+cos(x),y(x), singsol=all)
\[ y \left (x \right ) = \sin \left (2 x \right ) c_{2} +\cos \left (2 x \right ) c_{1} +\frac {x^{2}}{4}-\frac {1}{8}+\frac {\cos \left (x \right )}{3} \]
✓ Solution by Mathematica
Time used: 0.099 (sec). Leaf size: 36
DSolve[y''[x]+4*y[x]==x^2+Cos[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x^2}{4}+\frac {\cos (x)}{3}+c_1 \cos (2 x)+c_2 \sin (2 x)-\frac {1}{8} \\ \end{align*}