Internal problem ID [10268]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter VII, Linear differential equations with constant coefficients. Article 52. Summary.
Page 117
Problem number: Ex 13.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+y-x \cos \left (x \right )=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 29
dsolve(diff(y(x),x$2)+y(x)=x*cos(x),y(x), singsol=all)
\[ y \left (x \right ) = \sin \left (x \right ) c_{2} +c_{1} \cos \left (x \right )+\frac {\cos \left (x \right ) x}{4}+\frac {x^{2} \sin \left (x \right )}{4}-\frac {\sin \left (x \right )}{4} \]
✓ Solution by Mathematica
Time used: 0.011 (sec). Leaf size: 34
DSolve[y''[x]+y[x]==x*Cos[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{8} \left (\left (2 x^2-1+8 c_2\right ) \sin (x)+2 (x+4 c_1) \cos (x)\right ) \\ \end{align*}