Internal problem ID [5437]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 19. Linear equations with variable coefficients (Misc. types). Supplemetary
problems. Page 132
Problem number: 30.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_y]]
\[ \boxed {\left (2 x^{3}-1\right ) y^{\prime \prime \prime }-6 x^{2} y^{\prime \prime }+6 y^{\prime } x=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 19
dsolve((2*x^3-1)*diff(y(x),x$3)-6*x^2*diff(y(x),x$2)+6*x*diff(y(x),x)=0,y(x), singsol=all)
\[ y = c_{1} +c_{2} x^{2}+c_{3} x \left (x^{3}+4\right ) \]
✓ Solution by Mathematica
Time used: 1.357 (sec). Leaf size: 31
DSolve[(2*x^3-1)*y'''[x]-6*x^2*y''[x]+6*x*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {c_2 x^4}{4}+\frac {c_1 x^2}{2}-c_2 x+c_3 \]