Internal problem ID [5423]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 18. Linear equations with variable coefficients (Equations of second order).
Supplemetary problems. Page 120
Problem number: 32.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {\left (\sin \left (x \right ) x +\cos \left (x \right )\right ) y^{\prime \prime }-y^{\prime } \cos \left (x \right ) x +\cos \left (x \right ) y=x} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 23
dsolve((x*sin(x)+cos(x))*diff(y(x),x$2)-x*cos(x)*diff(y(x),x)+y(x)*cos(x)=x,y(x), singsol=all)
\[ y = \left (-\frac {c_{1} \cos \left (x \right )}{x}-\frac {\sin \left (x \right )}{x}+c_{2} \right ) x \]
✓ Solution by Mathematica
Time used: 0.764 (sec). Leaf size: 20
DSolve[(x*Sin[x]+Cos[x])*y''[x]-x*Cos[x]*y'[x]+y[x]*Cos[x]==x,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\sin (x)+c_1 x-c_2 \cos (x) \]