40.14.9 problem 30

Internal problem ID [6780]
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
Date solved : Monday, January 27, 2025 at 02:30:19 PM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} \left (2 x^{3}-1\right ) y^{\prime \prime \prime }-6 x^{2} y^{\prime \prime }+6 x y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.011 (sec). Leaf size: 20

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)
 

\[ y = c_3 \,x^{4}+c_2 \,x^{2}+4 c_3 x +c_1 \]

✓ Solution by Mathematica

Time used: 1.242 (sec). Leaf size: 31

DSolve[(2*x^3-1)*D[y[x],{x,3}]-6*x^2*D[y[x],{x,2}]+6*x*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {c_2 x^4}{4}+\frac {c_1 x^2}{2}-c_2 x+c_3 \]