Internal problem ID [5408]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 17. Linear equations with variable coefficients (Cauchy and Legndre).
Supplemetary problems. Page 110
Problem number: 8.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_y]]
\[ \boxed {x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }=x +\sin \left (\ln \left (x \right )\right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 43
dsolve(x^3*diff(y(x),x$3)+2*x^2*diff(y(x),x$2)=x+sin(ln(x)),y(x), singsol=all)
\[ y = -c_{1} \ln \left (x \right )-\frac {-\tan \left (\frac {\ln \left (x \right )}{2}\right )-1}{1+\tan \left (\frac {\ln \left (x \right )}{2}\right )^{2}}+\ln \left (x \right ) x -x +c_{2} x +c_{3} \]
✓ Solution by Mathematica
Time used: 0.173 (sec). Leaf size: 36
DSolve[x^3*y'''[x]+2*x^2*y''[x]==x+Sin[Log[x]],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} (\sin (\log (x))+\cos (\log (x))+2 ((-1+c_3) x+(x-c_1) \log (x)+c_2)) \]