29.11 problem Ex 13

Internal problem ID [10272]

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]]

Solve \begin {gather*} \boxed {y^{\prime \prime }+y-\cos \relax (x ) x=0} \end {gather*}

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)
 

\[ y \relax (x ) = \sin \relax (x ) c_{2}+\cos \relax (x ) c_{1}+\frac {\cos \relax (x ) x}{4}+\frac {\sin \relax (x ) x^{2}}{4}-\frac {\sin \relax (x )}{4} \]

Solution by Mathematica

Time used: 0.017 (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*}