Internal problem ID [5409]
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: 9.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _with_linear_symmetries]]
\[ \boxed {x^{3} y^{\prime \prime \prime }+y^{\prime } x -y=3 x^{4}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 25
dsolve(x^3*diff(y(x),x$3)+x*diff(y(x),x)-y(x)=3*x^4,y(x), singsol=all)
\[ y = \frac {x^{4}}{9}+c_{1} x +c_{2} \ln \left (x \right ) x +c_{3} \ln \left (x \right )^{2} x \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 31
DSolve[x^3*y'''[x]+x*y'[x]-y[x]==3*x^4,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {x^4}{9}+c_1 x+c_3 x \log ^2(x)+c_2 x \log (x) \]